The Resistor That Read High
A trainee in a DRDO electronics laboratory is checking a carbon-film resistor before soldering it into a 12 V DC indicator circuit. The four colour bands read Brown, Black, Red, Gold. The trainee calculates the value as 1,000 ohm with plus or minus 5% tolerance. A digital multimeter across the isolated resistor reads 1,180 ohm. With the resistor connected to the 12 V supply, a series ammeter reads 10.2 mA, whereas the trainee expected 12 mA for a 1 kohm resistor. The trainee concludes that the resistor is faulty and that the circuit probably has a short. The laboratory has a calibrated bench meter, a spare 1 kohm 1/4 W resistor, and a datasheet stating that the installed resistor is rated 1/8 W. The trainee asks you to confirm the diagnosis before replacing anything.
1. Calculate the tolerance limits and decide whether 1,180 ohm is acceptable. Show the arithmetic.
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The four-band code Brown-Black-Red-Gold means 10 x 100 = 1,000 ohm, with Gold giving plus or minus 5%. The limits are 1,000 - 50 = 950 ohm and 1,000 + 50 = 1,050 ohm. A reading of 1,180 ohm is 130 ohm above the upper limit, or 18% above nominal, so it is outside the stated tolerance. The resistor does not meet its marked specification.
2. Does the 10.2 mA reading support the 'short circuit' conclusion? Use Ohm's law and compare with the expected current.
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Expected current at 12 V and 1,000 ohm is I = V/R = 12/1000 = 12 mA. The measured 10.2 mA implies R = V/I = 12/0.0102 = about 1,176 ohm, which agrees with the multimeter reading. A short circuit would reduce resistance and increase current above 12 mA, not reduce it. The low current is consistent with a high resistance, so the short-circuit conclusion is unsupported.
3. Give the most likely explanation and the next diagnostic step, considering the 1/8 W rating.
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Power dissipation is P = V squared / R = 144/1180 = about 0.122 W. The resistor is rated 1/8 W = 0.125 W, so it is running at nearly its full rating; self-heating can drift a carbon-film resistor upward. The next step is to isolate the resistor, let it cool, and re-measure with the calibrated bench meter; if it stays near 1.18 kohm, replace it and use the 1/4 W spare for margin.