Question 535: Current Electricity

Question

When a galvanometer is shunted by a resistance ' $s$ ', its current capacity increases ' $n$ ' times. If the same galvanometer is shunted by another resistance ' $s_1$ ', its capacity will increase to ' $n_1$ ' times original current. The value of ' $n_1$ ' is

Accepted Answer

When a galvanometer is shunted with a resistance ' $s$ ', its current handling capacity increases by a factor of ' $n$ '. If this galvanometer is then shunted with a different resistance ' $s_1$ ', its capacity is enhanced to ' $n_1$ ' times the original current capacity.
Derivation
Shunt Resistance Formula
:
The formula for shunt resistance, when applied to a galvanometer, is:
$    s = G \left( \frac{1}{1 - \frac{I}{I_g}} ight)    $
Here, $ G $ represents the galvanometer constant, $ I $ is the total current, and $ I_g $ is the maximum current the galvanometer can handle initially.
Current Capacity Factor
:
The current capacity factor $ n $ is expressed as:
$    n = \frac{1}{I_g}    $
Therefore, using the relationship for shunt resistance:
$    s = G \left( \frac{1}{1-n} ight)    $
Rearranging the terms provides:
$    G = s (n - 1) \quad 	ext{(Equation i)}    $
Shunted with Another Resistance $s_1$
:
When the galvanometer is shunted with another resistance $s_1$, the new formula becomes:
$    s_1 = G \left( \frac{1}{1-n_1} ight)    $
Solving for $ n_1 $:
$    n_1 = \frac{G + s_1}{s_1}    $
Substituting Equation (i) into this:
$    n_1 = \frac{s(n-1) + s_1}{s_1}    $
This expression gives you the new current capacity factor ' $n_1$ ' when the galvanometer is shunted with the resistance ' $s_1$ '.

Answer

$\frac{(\mathrm{n}+\mathrm{s})}{\mathrm{s}_1}$

Answer

$\frac{s_1(n-s)-s_1}{s_1}$

Answer

$\frac{(n+1) s}{s_1}$

Answer

$\frac{\mathrm{s}(\mathrm{n}-1)+\mathrm{s}_1}{\mathrm{~s}_1}$

Current Electricity

When a galvanometer is shunted by a resistance ' s ', its current capacity increases ' n ' times. If the same galvanometer is shunted by another resistance ' s_1 ', its capacity will increase to ' n_1 ' times original current. The value of ' n_1 ' is

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