JEE Advanced · 2014 · 25 May 2014 · Paper 1 · Current Electricity

Two ideal batteries of

e m f V_{1}

and

V_{2}

and three resistances

R_{1}, R_{2}

and

R_{3}

are connected as shown in the figure. The current in resistance

R_{2}

would be zero if

Answer: (A), (B), (D)

Solution

Let current through

R_{1}

i

, through

R_{2}

i_{1}

, and through

R_{3}

i - i_{1}

.

Kirchhoff's voltage law:
Loop 1:

i R_{1} + i_{1} R_{2} = V_{1}

Loop 2:

i_{1} R_{2} - (i - i_{1}) R_{3} = - V_{2}

, which gives

i_{1} (R_{2} + R_{3}) - i R_{3} = - V_{2}

For

i_{1} = 0

: From loop 1,

i R_{1} = V_{1}

. From loop 2,

- i R_{3} = - V_{2}

, so

i R_{3} = V_{2}

.

Dividing:

\frac{R _{1}}{R _{3}} = \frac{V _{1}}{V _{2}}

, or

V_{1} R_{3} = V_{2} R_{1}

.

Checking options:
(A)

V_{1} = V_{2}

and

R_{1} = R_{3}

V_{1} R_{3} = V_{2} R_{1}

✓
(B)

V_{1} = V_{2}

and

R_{1} = R_{3}

V_{1} R_{3} = V_{2} R_{1}

✓
(C)

V_{1} = 2 V_{2}

and

R_{3} = 2 R_{1}

V_{1} R_{3} = 2 V_{2} \cdot 2 R_{1} = 4 V_{2} R_{1} \neq = V_{2} R_{1}

✗
(D)

2 V_{1} = V_{2}

and

R_{3} = 2 R_{1}

V_{1} R_{3} = V_{1} \cdot 2 R_{1} = 2 V_{1} R_{1} = V_{2} R_{1}

✓

JEE Advanced · 2014 · 25 May 2014 · Paper 1 · One or more correct options