First slide

Electrical power

Question

The ends of a resistor are connected to the terminals of a battery of internal resistance $1 Ω$ . If 75% of the power supplied by the battery is dissipated in the external resistor, find its resistance.

Moderate

A

1.5 $Ω$
B

4 $Ω$
C

2 $Ω$
D

3 $Ω$

Solution

$\begin{array}{l} i = E / (R + r) \\ Now i^{2} R = 75 % of Ei \\ \Rightarrow \frac{E^{2} R}{{(R + r)}^{2}} = \frac{3}{4} . \frac{E^{2}}{(R + r)} \Rightarrow 4 R = 3 (R + r) \Rightarrow R = 3 r \Rightarrow R = 3 \times 1 Ω = 3 Ω \end{array}$

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