If a resistance {R_2} is connected in paralle | vedclass

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(D) In the given circuit,the resistors $R$ and ${R_2}$ are connected in parallel. Let the current through $R$ be ${I_1}$. Then the current through ${R

Vedclass · Accepted Answer

$\frac{I}{2},\,R$

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(D) In the given circuit,the resistors $R$ and ${R_2}$ are connected in parallel. Let the current through $R$ be ${I_1}$. Then the current through ${R_2}$ is $(I - {I_1})$.Since they are in parallel,the potential difference across both resistors must be equal:${I_1}R = (I - {I_1}){R_2}$Rearranging for ${R_2}$,we get:${R_2} = \frac{{I_1}R}{I - {I_1}}$Now,we test the given options for the current through $R$ (which is ${I_1}$) and the resistance ${R_2}$:For option $(d)$,${I_1} = \frac{I}{2}$ and ${R_2} = R$:${R_2} = \frac{(\frac{I}{2})R}{I - \frac{I}{2}} = \frac{\frac{I}{2}R}{\frac{I}{2}} = R$This satisfies the condition. Thus,the correct option is $(d)$.

If a resistance ${R_2}$ is connected in parallel with the resistance $R$ in the circuit shown,then the possible value of current through $R$ and the possible value of ${R_2}$ will be:

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