Question

A certain amount of current when flowing in a properly set tangent galvanometer, produces a deflection of 450⁰. If the current be reduced by a factor of the deflection would

• A. Decrease by 30⁰
• B. Decreases by 15⁰
• C. Increase by 15⁰
• D. Increase by 30⁰

Answer 1

Answer: (B)

Decreases by 15⁰

Answer 2

By using

$\mathrm { i } \propto \tan \theta \Rightarrow \frac { \mathrm { i } _ { 1 } } { \mathrm { i } _ { 2 } } = \frac { \tan \theta _ { 1 } } { \tan \theta _ { 2 } } \Rightarrow \frac { \mathrm { i } _ { 1 } } { \mathrm { i } _ { 1 } / \sqrt { 3 } } = \frac { \tan 45 ^ { \circ } } { \tan \theta _ { 2 } }$

$\Rightarrow \sqrt { 3 } \tan \theta _ { 2 } = 1 \Rightarrow \tan \theta _ { 2 } = \frac { 1 } { \sqrt { 3 } } \Rightarrow \theta _ { 2 } = 30 ^ { \circ }$

So deflection will decrease by $45 ^ { \circ } - 30 ^ { \circ } = 15 ^ { \circ }$