A voltmeter has a resistance of $G$ ohms and range $V$ volts. The value of resistance used in series to conver

Question

A voltmeter has a resistance of $G$ ohms and range $V$ volts. The value of resistance used in series to convert it into a voltmeter of range $nV$ volts is:

Accepted Answer

1.  **Principle:** To increase the range of a voltmeter, a high resistance ($R$) is connected in series with the galvanometer (or existing voltmeter coil) .
2.  **Initial Condition:** Let $I_g$ be the current required for full-scale deflection. With resistance $G$ and range $V$, Ohm's law gives $V = I_g G$.
3.  **New Condition:** We want the new range to be $V' = nV$. We connect a resistance $R$ in series. The total resistance becomes $(G + R)$.
4.  **Equation:** The new voltage range corresponds to the same full-scale current $I_g$ flowing through the series combination:
    $V' = I_g (G + R)$
    Substituting $V' = nV$ and $I_g = V/G$:
    $nV = \frac{V}{G} (G + R)$
    $n = \frac{G + R}{G}$
    $n = 1 + \frac{R}{G}$
    $\frac{R}{G} = n - 1$
    $R = (n - 1)G$.

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