DC Circuits
DC circuits questions test series and parallel networks, Kirchhoff's laws, and meter behaviour. You must reduce networks to equivalent resistance and track which quantity is common in each connection.
Core rules
- Series: current is the same through every component; voltages add; resistances add.
- Parallel: voltage is the same across every branch; currents add; reciprocal resistances add: 1/R_eq = 1/R1 + 1/R2 + ...
- Kirchhoff's current law: current into a node equals current out.
- Kirchhoff's voltage law: algebraic sum of voltages around a closed loop is zero.
- Voltage divider: V_out = V_total × R_out / R_total for series resistors.
- Ammeters go in series with low resistance; voltmeters go in parallel with high resistance.
Worked example
A 4 Ω resistor is in series with a parallel pair of 6 Ω and 3 Ω across 12 V. Find the total current and branch currents. Parallel pair: 1/R_p = 1/6 + 1/3 = 1/2, so R_p = 2 Ω. R_total = 4 + 2 = 6 Ω; I_total = 12 / 6 = 2 A. Voltage across parallel pair = 2 A × 2 Ω = 4 V. Branch currents: 4/6 = 0.667 A and 4/3 = 1.333 A. Reasoning: reduce the parallel block first, then use the total current to find the shared voltage.
Traps
- Adding parallel resistances directly instead of using reciprocals.
- Assuming voltage is the same in series; it is not.
- Placing an ammeter in parallel or a voltmeter in series.
- Ignoring that branch currents in parallel split according to resistance.