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Question 1Electrical Fundamentals and Circuit Theory

In a purely resistive AC circuit, what is the phase relationship between the applied voltage and the current?

  1. The current leads the voltage by 90 degrees.
  2. The voltage leads the current by 90 degrees.
  3. The current leads the voltage by 45 degrees.
  4. The voltage and current are in phase. Correct answer.

Explanation

Resistance dissipates energy without storing it, so the voltage across a resistor and the current through it rise and fall together. There is no reactance to shift the phase, so the phase angle is zero.

Question 2Electrical Fundamentals and Circuit Theory

A 12 V source is connected across a 4 ohm resistor. What current flows through the resistor?

  1. 3 A Correct answer.
  2. 48 A
  3. 0.33 A
  4. 16 A

Explanation

Ohm's law states that current equals voltage divided by resistance. Dividing 12 V by 4 ohms gives 3 A. This is the fundamental relationship used throughout DC circuit analysis.

Question 3Electrical Fundamentals and Circuit Theory

Two resistors of 6 ohms and 3 ohms are connected in parallel. What is the equivalent resistance?

  1. 4.5 ohms
  2. 2 ohms Correct answer.
  3. 18 ohms
  4. 9 ohms

Explanation

For two parallel resistors, the reciprocal rule gives 1/Req = 1/6 + 1/3 = 1/2, so Req = 2 ohms. The equivalent is always smaller than the smallest branch resistance.

Question 4Electrical Fundamentals and Circuit Theory

What is the SI unit of electrical capacitance?

  1. Tesla
  2. Farad Correct answer.
  3. Weber
  4. Henry

Explanation

Capacitance is measured in farads, defined as one coulomb of stored charge per volt of potential difference. The unit honors Michael Faraday.

Question 5Electrical Fundamentals and Circuit Theory

Which quantity is defined as the rate at which electrical energy is transferred by a circuit?

  1. Electric charge
  2. Electric flux
  3. Electric potential
  4. Electric power Correct answer.

Explanation

Electric power is energy transferred per unit time, measured in watts, where one watt equals one joule per second. Charge, potential, and flux describe other electrical properties.

Question 6Electrical Fundamentals and Circuit Theory

A wire carries 2 A for 30 seconds. How much charge passes a cross-section of the wire?

  1. 15 C
  2. 32 C
  3. 0.067 C
  4. 60 C Correct answer.

Explanation

Charge equals current multiplied by time, so 2 A times 30 s equals 60 coulombs. One ampere is one coulomb per second.

Question 7Electrical Fundamentals and Circuit Theory

In a series circuit, which statement about current is true?

  1. The current is the same through every component. Correct answer.
  2. The current is zero in the largest resistor.
  3. The current divides among the components.
  4. The current doubles at each component.

Explanation

A series circuit provides only one path, so the same current must flow through every element. Voltage, not current, divides across series components.

Question 8Electrical Fundamentals and Circuit Theory

What is the approximate RMS value of a sinusoidal voltage with a peak value of 170 V?

  1. 120 V Correct answer.
  2. 85 V
  3. 340 V
  4. 170 V

Explanation

For a sine wave, the RMS value equals the peak value divided by the square root of two, approximately 0.707 times the peak. Multiplying 170 V by 0.707 gives about 120 V.

Question 9Electrical Fundamentals and Circuit Theory

Kirchhoff's voltage law is best described by which statement?

  1. The algebraic sum of currents at a node is zero.
  2. The algebraic sum of voltages around any closed loop is zero. Correct answer.
  3. The total power equals the product of voltage and current.
  4. The total resistance equals the sum of individual resistances.

Explanation

Kirchhoff's voltage law expresses energy conservation: traversing any closed loop returns to the same potential, so the signed voltage drops sum to zero. The current-law statement belongs to Kirchhoff's current law.

Question 10Electrical Fundamentals and Circuit Theory

A 10 V source drives a series circuit of 100 ohms and 150 ohms. What is the voltage across the 150 ohm resistor?

  1. 6 V Correct answer.
  2. 4 V
  3. 2.5 V
  4. 10 V

Explanation

Total resistance is 250 ohms, so current is 10 V divided by 250 ohms, or 0.04 A. The drop across 150 ohms is 0.04 A times 150 ohms, giving 6 V.

Question 11Electrical Fundamentals and Circuit Theory

What is the total capacitance of a 4 microfarad and a 12 microfarad capacitor connected in series?

  1. 3 microfarads Correct answer.
  2. 48 microfarads
  3. 8 microfarads
  4. 16 microfarads

Explanation

Series capacitors combine like parallel resistors: 1/C = 1/4 + 1/12 = 1/3, giving 3 microfarads. The equivalent is smaller than the smallest capacitor.

Question 12Electrical Fundamentals and Circuit Theory

An inductor of 0.2 H carries a current changing at 50 A per second. What magnitude of voltage is induced across the inductor?

  1. 0.1 V
  2. 250 V
  3. 0.004 V
  4. 10 V Correct answer.

Explanation

The inductor voltage equals inductance times the rate of change of current, v = L di/dt. Multiplying 0.2 H by 50 A/s gives 10 V.

Question 13Electrical Fundamentals and Circuit Theory

What is the time constant of a circuit containing a 100 ohm resistor and a 50 microfarad capacitor in series?

  1. 0.5 s
  2. 0.005 s Correct answer.
  3. 2 s
  4. 5000 s

Explanation

The RC time constant equals resistance times capacitance, so 100 ohms times 50 microfarads (5e-5 F) equals 0.005 seconds. This is the time to reach about 63 percent of final voltage.

Question 14Electrical Fundamentals and Circuit Theory

In a series RLC circuit at resonance, which condition holds?

  1. Total impedance is at its maximum.
  2. The phase angle is 90 degrees.
  3. Inductive reactance equals capacitive reactance. Correct answer.
  4. Capacitive reactance exceeds inductive reactance.

Explanation

Resonance occurs when inductive and capacitive reactances are equal in magnitude, so they cancel and the circuit becomes purely resistive. At that point impedance is minimal and the phase angle is zero.

Question 15Electrical Fundamentals and Circuit Theory

A 60 W lamp operates on 120 V. What is its resistance, assuming it behaves as a pure resistor?

  1. 0.5 ohms
  2. 240 ohms Correct answer.
  3. 2 ohms
  4. 7200 ohms

Explanation

Power equals voltage squared divided by resistance, so R = V^2/P = 14400/60 = 240 ohms. Alternatively, current is 0.5 A and R = 120/0.5.

Question 16Electrical Fundamentals and Circuit Theory

What is the reactive power in a purely inductive circuit carrying 2 A RMS at 120 V RMS?

  1. 60 VAR
  2. 0 VAR
  3. 240 VAR Correct answer.
  4. 120 VAR

Explanation

Reactive power equals voltage times current for a purely reactive load, so 120 V times 2 A gives 240 VAR. The power oscillates between source and inductor without net energy dissipation.

Question 17Electrical Fundamentals and Circuit Theory

Which statement correctly describes conventional current direction?

  1. It alternates regardless of source polarity.
  2. It flows from positive to negative terminals. Correct answer.
  3. It flows only in superconductors.
  4. It flows from negative to positive terminals.

Explanation

Conventional current is defined as the direction positive charge would move, from the positive terminal through the external circuit to the negative terminal. Electron flow is opposite to this convention.

Question 18Electrical Fundamentals and Circuit Theory

A circuit has two parallel branches of 6 ohms and 3 ohms across a 12 V source. What is the total current drawn from the source?

  1. 1.33 A
  2. 6 A Correct answer.
  3. 4 A
  4. 2 A

Explanation

Each branch sees the full 12 V, so branch currents are 2 A and 4 A. Summing them at the node gives 6 A total, consistent with an equivalent resistance of 2 ohms.

Question 19Electrical Fundamentals and Circuit Theory

The superposition theorem applies to which type of circuit?

  1. Only AC circuits at resonance
  2. Only circuits with a single source
  3. Linear circuits with multiple independent sources Correct answer.
  4. Only nonlinear circuits

Explanation

Superposition states that in a linear circuit with multiple independent sources, the total response is the sum of responses to each source acting alone. It relies on linearity, so nonlinear elements are excluded.

Question 20Electrical Fundamentals and Circuit Theory

Using Thevenin's theorem, a network is reduced to an equivalent circuit consisting of which elements?

  1. A capacitor in parallel with an inductor
  2. A voltage source in series with a resistor Correct answer.
  3. Two voltage sources in series
  4. A current source in parallel with a resistor

Explanation

Thevenin's theorem replaces any linear two-terminal network with a single voltage source in series with a resistance. Norton's theorem gives the dual current-source form.

Question 21Electrical Fundamentals and Circuit Theory

A capacitor of 10 microfarads is charged to 100 V. How much energy is stored?

  1. 0.1 J
  2. 0.05 J Correct answer.
  3. 1 J
  4. 0.005 J

Explanation

Energy stored in a capacitor is one half times capacitance times voltage squared. Half of 10 microfarads times 10000 V^2 equals 0.05 joules.

Question 22Electrical Fundamentals and Circuit Theory

What is the impedance magnitude of a series circuit with 30 ohms resistance and 40 ohms inductive reactance?

  1. 50 ohms Correct answer.
  2. 10 ohms
  3. 70 ohms
  4. 1200 ohms

Explanation

Impedance magnitude is the square root of R squared plus X squared. The square root of 900 plus 1600 equals the square root of 2500, which is 50 ohms.

Question 23Electrical Fundamentals and Circuit Theory

An ideal transformer has 200 primary turns and 50 secondary turns. If the primary voltage is 240 V, what is the secondary voltage?

  1. 60 V Correct answer.
  2. 48 V
  3. 120 V
  4. 960 V

Explanation

The voltage ratio equals the turns ratio, so secondary voltage is primary voltage times secondary turns divided by primary turns. That is 240 times 50/200, giving 60 V.

Question 24Electrical Fundamentals and Circuit Theory

A balanced three-phase load draws 10 A per phase at 400 V line-to-line with a power factor of 0.8. What is the total real power approximately?

  1. 8.0 kW
  2. 3.2 kW
  3. 13.9 kW
  4. 5.5 kW Correct answer.

Explanation

For a balanced three-phase load, real power equals the square root of three times line voltage times line current times power factor. Computing 1.732 times 400 times 10 times 0.8 gives about 5.5 kW.

Question 25Electrical Fundamentals and Circuit Theory

A resistor of 8 ohms and a capacitor with reactance of 6 ohms are in series across a 50 V AC source. What is the phase angle of the current relative to the voltage?

  1. The current lags by about 37 degrees.
  2. The current leads by about 53 degrees.
  3. The current leads by about 37 degrees. Correct answer.
  4. The current is in phase with the voltage.

Explanation

With capacitive reactance, the current leads the voltage. The angle is the arctangent of Xc/R, or arctangent of 6/8, which is about 37 degrees leading.

Question 26Electrical Fundamentals and Circuit Theory

Which quantity is defined as the rate of transfer of electrical energy, equal to the product of voltage and current in a resistive DC circuit?

  1. Magnetic flux density
  2. Electric power Correct answer.
  3. Capacitance
  4. Electric charge

Explanation

Electric power is the rate at which energy is transferred, and in a resistive DC circuit it equals voltage multiplied by current (P = VI). The other quantities describe stored charge, charge storage per volt, and magnetic field strength, none of which are energy transfer rates.

Question 27Electrical Fundamentals and Circuit Theory

A coil has 400 turns and a current of 0.5 A produces a flux of 2 mWb linking all turns. What is the inductance of the coil?

  1. 4 H
  2. 0.004 H
  3. 1.6 H Correct answer.
  4. 0.4 H

Explanation

Inductance is flux linkage divided by current: L = NΦ/I = (400 × 0.002)/0.5 = 0.8/0.5 = 1.6 H. The relationship links the total flux through all turns to the current producing it.

Question 28Electrical Fundamentals and Circuit Theory

A capacitor of 20 microfarads and a resistor of 5 kilohms are connected in series across a 12 V DC source, initially uncharged. What is the capacitor voltage 0.2 seconds after the switch is closed?

  1. 4.41 V
  2. 0 V
  3. 12 V
  4. 7.59 V Correct answer.

Explanation

The time constant is τ = RC = 5000 × 20×10⁻⁶ = 0.1 s, so 0.2 s is two time constants. The capacitor voltage follows v = V(1 − e^(−t/τ)) = 12(1 − e^−2) ≈ 12 × 0.8647 ≈ 7.59 V.

Question 29Electrical Fundamentals and Circuit Theory

In a circuit, a 6 V independent voltage source is connected in series with a 2 ohm resistor, and a 4 A independent current source is connected in parallel with a 3 ohm resistor across the same two nodes. Applying superposition, what is the current through the 3 ohm resistor?

  1. 6 A
  2. 4 A
  3. 2.4 A Correct answer.
  4. 1.2 A

Explanation

With the current source open, the 6 V source drives the 2 ohm and 3 ohm resistors in series, giving 6/5 = 1.2 A through the 3 ohm branch. With the voltage source shorted, the 4 A source divides between 3 ohm and 2 ohm branches, giving 4 × 2/5 = 1.6 A through the 3 ohm branch. Both contributions flow in the same direction, so the total is 1.2 + 1.6 = 2.4 A.

Question 30Electrical Fundamentals and Circuit Theory

Which statement best describes the function of a capacitor in a DC circuit once steady state is reached?

  1. It passes direct current while storing energy in its electric field.
  2. It blocks direct current while storing energy in its electric field. Correct answer.
  3. It converts direct current into alternating current through induction.
  4. It blocks direct current while storing energy in its magnetic field.

Explanation

A capacitor stores energy in the electric field between its plates and, at DC steady state, behaves as an open circuit because the dielectric prevents conduction. Energy storage in a magnetic field is characteristic of an inductor, not a capacitor.

Question 31Wiring Methods, Materials, and Installation Practices

When Type NM-B cable is run through bored holes in wood framing members, the cable must be protected by a listed bushing or be kept at least how far from the nearest edge of the hole?

  1. 3/4 in.
  2. 1-1/2 in.
  3. 2 in.
  4. 1-1/4 in. Correct answer.

Explanation

The NEC requires that where NM cable is run through bored holes in wood members, it must be kept at least 1-1/4 in. from the nearest edge of the hole, or else protected by a listed steel plate or bushing. This clearance prevents nails and screws driven into the framing from penetrating the cable.

Question 32Wiring Methods, Materials, and Installation Practices

A metal outlet box is installed in a wall with a drywall surface. Which condition requires the box to be provided with a listed extension ring or box extension?

  1. The box contains more than two conductors
  2. The box is set back so the finished surface leaves the box more than 1/4 in. recessed at combustible finish Correct answer.
  3. The box is mounted flush with the stud face
  4. The box is fed by a 20 A branch circuit

Explanation

Where a box is recessed behind a combustible finished surface, the box must be flush with or project beyond the surface, with limited setback permitted only for noncombustible finishes. Excessive setback exposes combustible material to heat and arcing and prevents proper support of the device and cover.

Question 33Wiring Methods, Materials, and Installation Practices

Which conductor is permitted to be identified by a continuous outer finish that is white or gray?

  1. The ungrounded conductor of a 3-way switch traveler
  2. The grounded conductor of a branch circuit Correct answer.
  3. The grounding electrode conductor
  4. The equipment grounding conductor

Explanation

White or gray is reserved for the grounded (neutral) conductor of a circuit. Equipment grounding conductors are identified by green, green with yellow stripes, or bare copper, and ungrounded conductors use other colors.

Question 34Wiring Methods, Materials, and Installation Practices

Type AC cable installed in a run must be supported and secured at intervals not exceeding what distance?

  1. 10 ft
  2. 4-1/2 ft Correct answer.
  3. 6 ft
  4. 3 ft

Explanation

Armored cable must be secured and supported at intervals not exceeding 4-1/2 ft and within 12 in. of every box or fitting. This spacing keeps the cable from sagging and limits strain at terminations.

Question 35Wiring Methods, Materials, and Installation Practices

Nonmetallic-sheathed cable is permitted to be installed in which of the following locations without additional protection?

  1. Exposed in an area subject to physical damage
  2. Concealed within a wall of a dwelling unit Correct answer.
  3. Inside a duct used for ventilation air
  4. In a hoistway of a passenger elevator

Explanation

NM cable is commonly permitted concealed in walls, floors, and ceilings of dwellings. It is prohibited in ducts, plenums, hoistways, and locations where it would be subject to physical damage unless protected.

Question 36Wiring Methods, Materials, and Installation Practices

A rigid metal conduit run is being installed outdoors in a corrosive industrial atmosphere. Which characteristic makes RMC a suitable choice in this environment?

  1. Its lightweight aluminum threads require no bonding
  2. Its thick-walled galvanized steel construction resists corrosion and physical damage Correct answer.
  3. Its nonmetallic lining isolates the conductors
  4. Its flexible jacket absorbs vibration

Explanation

Rigid metal conduit is a thick-wall raceway, often galvanized, providing mechanical protection and corrosion resistance suitable for harsh environments. Its threads also allow it to serve as an equipment grounding conductor when properly made up.

Question 37Wiring Methods, Materials, and Installation Practices

When installing surface metal raceway, the raceway must be supported at intervals not exceeding what distance unless the raceway is specifically listed for a greater spacing?

  1. 3 ft
  2. 4-1/2 ft
  3. 10 ft Correct answer.
  4. 6 ft

Explanation

Surface metal raceway generally must be supported at intervals not exceeding 10 ft, with additional support near boxes and fittings per the listing. The manufacturer's listing may permit other spacing.

Question 38Wiring Methods, Materials, and Installation Practices

Which of the following is the minimum size copper conductor permitted for a branch circuit supplying a single receptacle on a 20 A circuit in a commercial occupancy?

  1. 18 AWG
  2. 14 AWG
  3. 12 AWG Correct answer.
  4. 16 AWG

Explanation

A 20 A branch circuit requires conductors with an ampacity of at least 20 A, which corresponds to 12 AWG copper. 14 AWG is limited to 15 A circuits, and smaller sizes are not permitted for this application.

Question 39Wiring Methods, Materials, and Installation Practices

A 3/4 in. electrical metallic tubing run contains four 8 AWG THHN conductors. What is the primary purpose of limiting the number of conductors in the raceway?

  1. To control heat generated by current-carrying conductors and protect conductor insulation Correct answer.
  2. To keep the total weight of the raceway within support limits
  3. To prevent the raceway from serving as a grounding conductor
  4. To ensure the conductors can be identified by color

Explanation

Raceway fill limits are based on heat dissipation: bundled conductors cannot shed heat as readily, so ampacity must be adjusted and fill restricted. The rules also ensure conductors can be pulled without damage to insulation.

Question 40Wiring Methods, Materials, and Installation Practices

A metal raceway is used as the equipment grounding conductor. Which condition must be met at every joint to ensure a continuous, effective ground-fault current path?

  1. The raceway must be mechanically and electrically continuous, with bonding jumpers where required around fittings that may not be reliably conductive Correct answer.
  2. The raceway must contain an insulated neutral conductor
  3. The raceway must be supported every 3 ft
  4. The raceway must be painted at each coupling

Explanation

When a raceway serves as the equipment grounding conductor, all joints must maintain electrical continuity, and bonding jumpers are required around components that could interrupt the path. This ensures a low-impedance return path for fault current.

Question 41Wiring Methods, Materials, and Installation Practices

A 1-gang box is installed in a ceiling and contains a luminaire with a fixture wire and a splice of two 12 AWG conductors. What must be verified before the installation is complete?

  1. That the box is listed for ceiling use only
  2. That the box is bonded to a grounding electrode
  3. That the box volume is sufficient for all conductors, devices, and fittings counted under the fill rules Correct answer.
  4. That the luminaire is controlled by a dimmer

Explanation

Box fill calculations must account for each conductor, the device or luminaire, and fittings using the volume allowances in the code. An undersized box can damage insulation and create a fire hazard.

Question 42Wiring Methods, Materials, and Installation Practices

Which wiring method is permitted for the exposed interior wiring in a commercial garage where vehicles are repaired?

  1. Rigid metal conduit or intermediate metal conduit Correct answer.
  2. Nonmetallic-sheathed cable
  3. Surface raceway with a nonmetallic cover
  4. Type SJ cord supported every 6 ft

Explanation

Commercial garages require wiring methods with a higher degree of physical protection, and RMC or IMC are accepted. NM cable and flexible cords are not permitted as fixed wiring in these occupancies.

Question 43Wiring Methods, Materials, and Installation Practices

A conduit body is installed in a run of EMT and contains a splice. Which requirement applies to the conduit body?

  1. It must be listed and marked with its cubic-inch capacity, and the contained conductors must not exceed that volume Correct answer.
  2. It must be supported only by the conduit on one side
  3. It must be buried underground without protection
  4. It must be a minimum of 24 in. long

Explanation

Conduit bodies used as pulling points or for splices must be listed, and the number and size of conductors must not exceed the marked capacity. Sizing by cubic inches ensures adequate space and heat dissipation.

Question 44Wiring Methods, Materials, and Installation Practices

A 20 A circuit is wired with 12 AWG copper conductors in a raceway. The equipment grounding conductor is required to be what minimum size?

  1. 12 AWG copper Correct answer.
  2. 16 AWG copper
  3. 10 AWG copper
  4. 14 AWG copper

Explanation

The equipment grounding conductor must be sized according to the overcurrent device rating, and for a 20 A circuit the minimum copper size is 12 AWG. It may be larger if the circuit conductors are increased in size.

Question 45Wiring Methods, Materials, and Installation Practices

Which of the following best describes the requirement for securing Type MC cable with an interlocking metal tape armor?

  1. It must be secured at intervals not exceeding 3 ft with no requirement near boxes
  2. It requires no securing when run exposed
  3. It must be supported only by its terminations
  4. It must be secured at intervals not exceeding 6 ft and within 12 in. of boxes, unless the cable is listed and identified for support at greater intervals Correct answer.

Explanation

Type MC cable generally must be secured at intervals not exceeding 6 ft and within 12 in. of boxes and fittings. Cables specifically listed for other support spacing may follow the listing.

Question 46Wiring Methods, Materials, and Installation Practices

A feeder is installed in a rigid PVC conduit that will be exposed to direct sunlight on a rooftop. Which consideration affects the selection and installation of the raceway?

  1. The conduit must be filled to 100 percent of its area
  2. PVC cannot be used outdoors under any condition
  3. PVC must be painted black to increase rigidity
  4. The raceway must be listed and identified for sunlight exposure, and expansion fittings must account for thermal expansion Correct answer.

Explanation

Rigid PVC exposed to sunlight must be listed and marked as sunlight resistant, and its high coefficient of thermal expansion requires expansion fittings. Paint can also be used to protect against ultraviolet degradation.

Question 47Wiring Methods, Materials, and Installation Practices

In a dwelling unit, a receptacle is installed in a kitchen countertop wall. Which requirement applies to the small-appliance branch circuits serving this area?

  1. The receptacles must be supplied by a 30 A circuit
  2. The receptacles must be supplied by at least two 20 A small-appliance branch circuits Correct answer.
  3. The receptacles must be on a circuit shared with the lighting outlet
  4. The receptacles may be supplied by a single 15 A circuit

Explanation

Kitchen countertop receptacles must be served by at least two 20 A small-appliance branch circuits, and these circuits may not supply other outlets except as permitted. This limits overload and improves reliability.

Question 48Wiring Methods, Materials, and Installation Practices

A metal-clad cable is terminated in a box using a connector. What is required to ensure the armor does not carry fault current improperly?

  1. The armor must be isolated from the box
  2. The armor must be bonded to the box through a listed connector, and any internal bonding strip must be connected to the grounding terminal Correct answer.
  3. The cable must be derated by 50 percent
  4. The connector must be nonmetallic

Explanation

The armor of MC cable is not by itself an adequate fault-current path unless bonded; listed connectors and the internal bonding strip provide continuity to the equipment grounding terminal. This ensures fault current returns to the source.

Question 49Wiring Methods, Materials, and Installation Practices

A junction box is installed in a wet location. Which of the following describes the appropriate enclosure selection?

  1. A box with open knockouts facing upward
  2. A listed enclosure marked for wet locations with gasketed covers and suitable hubs Correct answer.
  3. A box listed for dry locations only
  4. A standard sheet-metal box with no gasket

Explanation

Enclosures in wet locations must be listed for that environment, typically with gaskets and threaded or gasketed entries. Water intrusion can cause corrosion and ground faults.

Question 50Wiring Methods, Materials, and Installation Practices

A conduit run passes through a fire-rated wall assembly. What is the key requirement for the penetration?

  1. The conduit must be painted red
  2. The conduit must be filled with sand
  3. The penetration must be sealed with an approved firestop system tested for that assembly Correct answer.
  4. The penetration must be left open for ventilation

Explanation

Penetrations of fire-rated assemblies must be protected with an approved firestop system matching the tested assembly to maintain the fire-resistance rating. Leaving the annular space open compromises the barrier.