Question

A battery of e.m.f. 12V and internal resistance $2\Omega$ is connected in series with a tangent galvanometer of resistance $4\Omega$. The deflection is $60^\circ$ when the plane of the coil is along the magnetic meridian. To get a deflection of $30^\circ$, the resistance to be connected in series with the tangent galvanometer is :

• A. 16 $\Omega$
• B. 20 $\Omega$
• C. 10 $\Omega$
• D. 5 $\Omega$

Answer 1

Answer: (A)

16 $\Omega$

Answer 2

Using, I = K tan $\theta$, we get $\frac{12}{(4 + 2)}$ K = tan 60$\circ$ or 2 = K $\times$ 1.7321 or K = $\frac{2}{1.7321}$ Again, for new situation $\frac{12}{(2 + R)}$ = K tan 30$^\circ$ = $\frac{2}{1.7321} \times 0.5774$ = 0.67 or $\frac{12}{0.67}$ = 2 + R or R = $\frac{12}{0.67}$ -2 or R = 18 - 2 = 16 $\Omega$