Four resistors , ,

PHYSICS · Subjective · A Level · Physics · Electricity · Electricity

Problem

Four resistors

R_1

R_2

R_3

, and

R_4

form the sides of a rectangle

A

–

B

–

C

–

D

–

A

in that order. A galvanometer of resistance

R_g

is connected between nodes

B

and

D

. An ideal cell of emf

E

is connected with its positive terminal at node

A

and its negative terminal at node

C

. (i) Assign mesh currents

I_1

in loop

A

–

B

–

D

–

A

and

I_2

in loop

B

–

C

–

D

–

B

. Write the two independent closed-path equations and the junction equation at node

B

. (ii) Solve these equations algebraically to obtain an expression for the galvanometer current

I_g

in terms of

E

R_1

R_2

R_3

R_4

, and

R_g

. (iii) Show that

I_g = 0

when

R_1/R_2 = R_3/R_4

, and state the practical significance of this condition.