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  • Two ideal batteries of emf  and and three

Two ideal batteries of emf V_1 and V_2 and three resistances R_1, R_2 and R_3 are connected. The current in Resistance R_3 would be zero if:-

Option: 1

\frac{V_1}{R_1}=\frac{V_2}{R_2}


Option: 2

\frac{V_1}{R_2}=\frac{V_2}{R_1}


Option: 3

R_3 is zero.


Option: 4

R_2 is zero.


Answers (1)

best_answer

Apply kirchoff's loop law,

In loop 1,

\begin{aligned} & V_1-i R_1-i, R_3=0 \\ & \frac{V_1-i R_1}{R_3}=i_1 \end{aligned}

In loop 2,

\begin{aligned} & i_1 R_3+V_2-\left(i-i_1\right) R_2=0 \\ & i_1 R_3+V_2-i R_2+i_1 R_2=0 \\ & i_1\left(R_2+R_3\right)=i R_2-V_2 \\ & i_1=\frac{i R_2-V_2}{R_2+R_3} . \end{aligned}

For i_1=0

\begin{array}{ll} V_1-i R_1=0 & \text { and } \quad i R_2-V_2=0 \\ i=\frac{V_1}{R_1} & \quad l=\frac{V_2}{R_2} \end{array}

Means \frac{V_1}{R_1}=\frac{V_2}{R_2}

Posted by

Kuldeep Maurya

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