Question 568: Current Electricity

Question

Two galvanometers $A$ and $B$ require currents of 4 mA and 7 mA , respectively to produce the same deflection of 20 divisions. If $S_A$ and $S_B$ are their sensitivities respectively, then

Accepted Answer

The sensitivity of a galvanometer is defined as the deflection per unit current. Mathematically, sensitivity ($S$) can be expressed as:
$$ S = \frac{	ext{deflection (divisions)}}{	ext{current (A)}} $$
For galvanometer $A$:
Deflection = 20 divisions
Current required = 4 mA = 0.004 A
Thus, the sensitivity of galvanometer $A$, $S_A$, is:
$$ S_A = \frac{20 	ext{ divisions}}{0.004 	ext{ A}} = 5000 	ext{ divisions/A} $$
For galvanometer $B$:
Deflection = 20 divisions
Current required = 7 mA = 0.007 A
Therefore, the sensitivity of galvanometer $B$, $S_B$, is:
$$ S_B = \frac{20 	ext{ divisions}}{0.007 	ext{ A}} \approx 2857.14 	ext{ divisions/A} $$
Comparing $S_A$ and $S_B$, we have:
$$ S_A = 5000 	ext{ divisions/A} > S_B = 2857.14 	ext{ divisions/A} $$
Thus, the correct answer is Option B: $S_A > S_B$.

Answer

$S_A< S_B$

Answer

$S_A>S_B$

Answer

$S_B=\frac{7}{4}=S_A$

Answer

$S_A=S_B=\frac{4}{7}$

Current Electricity

Two galvanometers A and B require currents of 4 mA and 7 mA , respectively to produce the same deflection of 20 divisions. If S_A and S_B are their sensitivities respectively, then

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