Equipment Rack Fault: Reading Voltages in a Series-Parallel 24 V Circuit
A 24-volt DC panel feeds an equipment rack. A 6-ohm resistor R1 is in series with a parallel pair: R2, a 12-ohm heater element, and R3, a 12-ohm lamp assembly. With the rack working normally the panel ammeter reads 2.0 amperes. During a check the lamp does not light and the heater is noticeably hotter than usual. A technician takes these readings with the panel energized: 8.0 volts across R1; 16 volts across the parallel pair; 16 volts across R3; no current in the R3 branch; about 1.33 amperes through R2. The rack must be back in service within 90 minutes. Spares on hand: one lamp assembly, one heater element, and a replacement 6-ohm resistor. The technician is working alone and has a clamp-on ammeter and a digital multimeter. The last maintenance report notes the lamp assembly was replaced eight months ago after a similar complaint.
1. Confirm the normal operating values of the rack so the readings can be judged against a known baseline.
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Parallel pair. Two equal 12-ohm branches: 12 / 2 = 6 ohms. (Product over sum: 144 / 24 = 6.)
Total resistance. R1 plus the pair: 6 + 6 = 12 ohms.
Total current. I = 24 / 12 = 2.0 amperes, which matches the ammeter.
Voltage drops. Across R1: 2 x 6 = 12 volts. Across the pair: 2 x 6 = 12 volts. The two drops sum to the 24-volt source.
Branch currents. 12 volts across each 12-ohm branch gives 1.0 ampere per branch, splitting the 2.0 amperes.
Heater power. 12 volts squared over 12 ohms = 12 watts.
2. Diagnose the fault from the readings, and explain why the heater is hotter while the lamp is dark.
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Total current from the R1 drop. 8.0 volts across 6 ohms means 8 / 6 = 1.33 amperes flowing, not 2.0. Current has fallen, so resistance has risen.
What the remaining current is doing. The only current path left is R2: 1.33 x 12 = 16 volts, which matches the measured 16 volts across the pair and across R3.
The R3 reading is a phantom. A voltmeter across an open branch reads the voltage present at that point because almost no current flows through the meter. Sixteen volts across R3 with zero current means the break is in R3's branch, not a supply failure.
Why the heater is hotter. Heater power is now 16 squared over 12 = 21.3 watts instead of 12 watts, roughly 78 percent over normal. That is why the heater is hot and the lamp is dark. Do not replace R1 or R2 on this evidence; both are consistent with a healthy 6-ohm and 12-ohm element.
3. Given a 90-minute window and one technician, what should be done first, what should not be done, and how is the repair verified?
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First. De-energize the panel and tag it. A resistance check across the lamp socket confirms the diagnosis: an open circuit where 12 ohms should be. Inspect the socket and connector for corrosion or a backed-out pin, since the lamp was replaced eight months ago for a similar complaint and a repeat failure points at the socket, not the lamp. Fit the spare lamp assembly only after the socket checks out.
Do not. Do not leave the rack running on one branch while deciding. The heater is dissipating about 21 watts against a 12-watt design, and a failed heater element turns a 20-minute lamp swap into a two-casualty repair. Do not swap R1 or R2 speculatively, and do not trust the 16 volts at R3 as proof that the lamp is being supplied.
Verify. Re-energize and confirm 2.0 amperes total, 12 volts across R1 and 12 volts across the pair, about 1.0 ampere in each branch. That restores the baseline and leaves time in the window to log the repeat failure for follow-up.