A coil consists of 1000 turns of copper wire having a cross-sectional area of 0.8 mm2. The mean length per turn is
80 cm and the resistivity of copper is 0.02 μΩ-m. What are the values of resistance of the coil and power absorbed by the coil when connected across 100 V DC supply respectively?

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UPSC ESE (Prelims) Electronics and Telecommunication Engineering 19 Feb 2023 Official Paper

Answer 1

The resistance of the coil can be calculated by using this formula:

$R = \rho\times \frac{L}{A}\times N$

Where:

$R$ = resistance.
$ρ$ = 0.02 μΩ-m resistivity of copper
$L$ = 80 cm = (0.8m)mean length per turn.
$A$ = 0.08mm²cross-sectional area.
$N$ = number of turns (1000).
R = $\frac{0.02\times10^{-6}\times 1000\times 80\times10^{-2}}{0.8\times10^{-6}}$
R = 20 Ω
The resistance of the coil is 20 Ω.
Now, to find the power absorbed by the coil when connected across a 100 V DC supply, we can use the formula: $<math xmlns="/"><semantics><mrow><mi>�</mi><mo>=</mo><mfrac><msup><mi>�</mi><mn>2</mn></msup><mi>�</mi></mfrac></mrow></semantics></math>$
$P = \frac{V^2}{R}$
Where,
$P$ = power
$V$ = voltage (100 V)
$�$ = resistance (20 Ω)
Power = 500 W.
Therefore, when connected across a 100 V DC supply, the power absorbed by the coil is $500 W$ .
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