Question

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✴️Two electric circuits 1 and 2 are shown in figure.3.55. In circuit 1 , key K is closed whereas in circuit 2 , key is open. Compare the currents in circuit 1 and 2

Class - 10th
Chapter - Electricity

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Answer 1

$\sf \Large Solution!!$

$\sf \large In\:circuit\:1$

$\sf \to K\:is\:closed$$\sf \to R_{1}\:and\:R_{2}\:are\:in\:parallel\:combinaion$

$\sf \to Equivalent\:resistance(R_{p})=\dfrac{R_{1}R_{2}}{(R_{1}+R_{2})}$

$\sf \to Current\:in\:the\:circuit(I_{1})=\dfrac{V}{R_{p}}$

$\sf \to Current\:in\:the\:circuit(I_{1})=\dfrac{V(R_{1}+R_{2})}{R_{1}R_{2}}$

$\sf$

$\sf \large In\:circuit\:2$

$\sf \to K\:is\:open$$\sf \to The\:resistance(R_{2})\:is\:out\:of\:the\:circuit$

$\sf \to Net\:resistance=R_{1}$

$\sf \to Current\:in\:the\:circuit(I_{2})=\dfrac{V}{R_{1}}$

$\sf \large So,$

$\sf \to \dfrac{I_{1}}{I_{2}}=\dfrac{\cancel{V}(R_{1}+R_{2})}{\cancel{R_{1}}R_{2}}\times \dfrac{\cancel{R_{1}}}{\cancel{V}}=\dfrac{(R_{1}+R_{2})}{R_{2}}$

$\sf (R\:equivalent)_{1}<(R\:equivalent)_{2}$

$\sf \boxed{Current\:of\:circuit\:1>Current\:of\:circuit\:2}$

Answer 2

$\tt\huge{\underline{\underline{ANSWER}}}$

It is given that in circuit 1, key is closed so current will flow through both the resistors and total current will be divided in parellel connection of resistors.

Whereas in 2nd circuit it is given that key for R2 is opened so current will not flow through R2 and current will not divide among resistors even in parellel connection and hence the total current will remain unchanged in R1.

$\boxed{\sf Total\: current\: in\: 1 \:>\:Total\: current\: in\: 2.}$