A DC source with internal resistance $R_0$ is connected to three identical resistors each of resistance $R$…

A DC source with internal resistance $R_0$ is connected to three identical resistors each of resistance $R$ as shown in the figure. If the thermal power generated in the circuit is highest, then

1. $R=2 R_0$
2. $R=3 R_0$
3. $R=\frac{R_0}{3}$
4. $R=R_0$

Solution

For maximum power, $R_0=R_{\mathrm{eq}}$ of circuit.
Given, resistances are in parallel combination, the equivalent value is $ \begin{aligned} & \frac{1}{R_{\mathrm{eq}}}=\frac{1}{R_0}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}=\frac{3}{R} \\ \Rightarrow \quad R_0 & =\frac{R}{3} \text { or } R=3 R_0 . \end{aligned} $

Asked in: AP EAMCET 2018 (23 Apr Shift 1)

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