First slide

Electrical power

Question

Three equal resistances each of R ohm are connected as shown in fig. A battery of 2 V and internal resistance 0 .1 ohm is connected across the circuit.
The value of R for which the heat generated in the circuit will be maximum is

Moderate

A

0.3 $Ω$
B

0.01 $Ω$
C

0.1 $Ω$
D

0.03 $Ω$

Solution

The three resistances are connected in parallel across the source. Their equivalent resistance
$R^{'} = \frac{R}{3}$
Current in the circuit, $i = \frac{2}{R^{'} + 0 \cdot 1}$
Heat produced, H = i² R' = $\frac{4 R^{'}}{{(R^{'} + 0 \cdot 1)}^{2}}$
Heat will be maximum when $\frac{dH}{{dR}^{'}} = 0$
Thus $\frac{d}{{dR}^{'}} [\frac{4 R^{'}}{{(R^{'} + 0 \cdot 1)}^{2}}] = 0$
Solving, we get R = $0 \cdot 1 Ω$
$∴$ R = 3R' = 3 x 0.1= 0.3 $Ω$

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