For the circuit shown in the figure, we have to find (a) the value of R so that the current in the circuit is 50 mA. We may take , , and (b) We have to find the rate at which internal energy appears in R.

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In the circuit shown in the figure

,

,

and

As

, the direction of the current in the circuit will be counter-clockwise. Let the current in the circuit be i A. We go round the circuit in the counter-clockwise direction and write the algebraic equation for the potential changes. We have

As we have

We want current, i, in the circuit to be 50 mA. Therefore, the value of R should be

(b)

Rate at which internal energy appears in R will be the Joule heat, and is given by the equation