Numerical explaning to find multiplying factor (07:58)

Lecture Notes :-

Q. A galvanometer with a full scale current of 10mA has a resistance of 1000Ω. The multiplying power (the ratio of measured current to
galvanometer current) of 100Ω shunt with this galvanometer is [2004]

(a) 110

(b) 100

(c) 11

(d) 10

Ans.

Given :- I_fs = I_m = 10 mA

R_m = 1000 Ω

R_sh = 100 Ω

m= ?

Solution :- The formula for calculating multiplying factor is given by,

m= measured current / galvanometer current = I/I_m

I_sh R_sh = I_m R_m —-(i)

I = I_m + I_sh

I_sh = I – I_m

(I-I_m) R_sh = I_m R_m

IR_sh – I_m R_sh = I_m R_m

IR_sh = I_m R_sh + I_m R_m

IR_sh = I_m (R_sh + R_m)

\frac{I}{I_{m}}=\frac{R_{sh}+R_{m}}{R_{sh}}=m m=\frac{100+1000}{100}=11

Therefore, option (c) is the correct answer.