MC Voltmeter Range Extension Calculation

To extend the voltage range of a Moving Coil (MC) voltmeter, an additional resistance, known as a series multiplier resistance, is connected in series with the voltmeter's internal resistance. This series resistor limits the current flowing through the meter movement, allowing it to measure higher voltages without exceeding its full-scale deflection current.

Let's define the parameters given in the question:

• Original full-scale voltage of the voltmeter, $V_m = 100$ V.
• Internal resistance of the voltmeter, $R_m = 2 \Omega$.
• Desired extended voltage range, $V = 200$ V.
• Additional series resistance required, $R_s$ (what we need to find).

The full-scale deflection current ($I_m$) is the maximum current the meter can handle, which occurs at the original full-scale voltage. This current can be calculated using Ohm's law:

$\qquad I_m = \frac{V_m}{R_m}$

Substituting the given values:

$\qquad I_m = \frac{100 \text{ V}}{2 \Omega} = 50 \text{ A}$

When the voltmeter's range is extended to $V = 200$ V by adding a series resistance $R_s$, the total resistance in the circuit becomes $R_m + R_s$. At the new full-scale voltage ($V$), the current flowing through the meter must still be the full-scale deflection current ($I_m$).

$\qquad V = I_m \times (R_m + R_s)$

We can substitute the expression for $I_m$ back into this equation:

$\qquad V = \left(\frac{V_m}{R_m}\right) \times (R_m + R_s)$

Now, we can rearrange this formula to solve for the additional series resistance $R_s$:

$\qquad \frac{V \cdot R_m}{V_m} = R_m + R_s$

$\qquad R_s = \frac{V \cdot R_m}{V_m} - R_m$

$\qquad R_s = R_m \left(\frac{V}{V_m} - 1\right)$

This formula shows that the required series resistance depends on the internal resistance of the meter and the ratio of the new range to the original range (the range multiplier, $m = V/V_m$).

Let's plug in the given values:

• $V_m = 100$ V
• $R_m = 2 \Omega$
• $V = 200$ V

$\qquad R_s = 2 \Omega \left(\frac{200 \text{ V}}{100 \text{ V}} - 1\right)$

$\qquad R_s = 2 \Omega (2 - 1)$

$\qquad R_s = 2 \Omega (1)$

$\qquad R_s = 2 \Omega$

Therefore, the additional resistance to be connected in series with the voltmeter is $2 \Omega$.