Question 93: Current Electricity

Question

Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3 are connected as shown in the figure. The current in resistance R2 would be zero if

Accepted Answer

Let i
1
and i
2
be the currents as shown in the figure.
Apply Kirchhoff's law in the loop ABCDA and CEFDC to get
$${i_1}{R_1} + ({i_1} - {i_2}){R_2} = {V_1}$$ ..... (1)
$${i_2}{R_3} - ({i_1} - {i_2}){R_2} = {V_2}$$ ...... (2)
Multiply equation (1) by R
3
and (2) by R
1
and then subtract to get the current through R
2
as
$$({i_1} - {i_2}) = {{{V_1}{R_3} - {V_2}{R_1}} \over {{R_1}{R_3} + {R_2}{R_3} - {R_1}{R_2}}}$$.
The current through R
2
becomes zero when V
1
R
3
= V
2
R
1
.

Answer

V1 = V2 and R1 = R2 = R3

Answer

V1 = V2 and R1 = 2R2 = R3

Answer

V1 = 2V2 and 2R1 = 2R2 = R3

Answer

2V1 = V2 and 2R1 = R2 = R3

Current Electricity

Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3 are connected as shown in the figure. The current in resistance R2 would be zero if

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