First slide

ammeter

Question

A moving coil galvanometer converted into an ammeter reads up to 0.03 A by connecting a shunt of resistance 4r across it and ammeter reads up to 0.06 A, when a shunt of resistance r is used. What is the maximum current which can be sent through this galvanometer if no shunt is used?

Moderate

A

0.03 A
B

0.04 A
C

0.02 A
D

0.01 A

Solution

Let G be the resistance of galvanometer and i_g the current which on passing through the galvanometer produces full-scale deflection.
Since G and S are in parallel, the potential difference across them will be
$\begin{array}{l} i_{g} \times G = (i - i_{g}) \times S \\ \frac{i_{g}}{i} = \frac{S}{S + G} \end{array}$
Hence, $i_{g} = \frac{4 r}{4 r + G} \times 0 .03 . ... (1)$
$i_{g} = \frac{r}{r + G} \times 0 .06 . ... (2)$
Equating Eqs. (1) and (2), we get
4r + G = 2(r + G)
$\begin{array}{l} \Rightarrow G = 2 r \\ ∴ i_{g} = \frac{4 r}{4 r + 2 r} \times 0 .03 = 0 .02 A [from Eq . (1)] \end{array}$

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