Question

A PMMC instrument has full-scale deflection current of \(50\ \mu\text{A}\) and coil resistance of \(1\ \text{k}\Omega\). The resistance to be added in series to convert it into 10 V voltmeter is

• A. \(99\ \text{k}\Omega\)
• B. \(199\ \text{k}\Omega\)
• C. \(299\ \text{k}\Omega\)
• D. \(399\ \text{k}\Omega\)

Hint:

Alternatively, use total resistance directly: \(R_{\text{total}} = \frac{V_{\text{new}}}{I_{fs}} = \frac{10\text{ V}}{50\ \mu\text{A}} = 200\ \text{k}\Omega\). Since the meter already has an internal resistance of \(1\ \text{k}\Omega\), the added series resistance is simply \(200\ \text{k}\Omega - 1\ \text{k}\Omega = 199\ \text{k}\Omega\).

Answer 1

The Correct Option is B

Concept: To extend the voltage measurement range of a Permanent Magnet Moving Coil (PMMC) instrument to act as a voltmeter, a high resistance called a multiplier (\(R_{se}\)) must be connected in series with the meter coil. The value of this series resistance is calculated using the multiplier multiplying factor equation: \[ R_{se} = R_m(m - 1) \] where:
• \(R_m\) is the internal coil resistance of the meter.
• \(m\) is the voltage multiplication factor, defined as \(m = \frac{V}{v_m}\).
• \(V\) is the required full-scale voltage range.
• \(v_m\) is the voltage drop across the meter coil at full-scale deflection current \(I_{fs}\) (\(v_m = I_{fs} \cdot R_m\)).

Step 1: Calculate the base voltage drop across the meter coil (\(v_m\)). Given parameters:
• Meter coil internal resistance (\(R_m\)) = \(1\ \text{k}\Omega = 1000\ \Omega\)
• Full-scale deflection current (\(I_{fs}\)) = \(50\ \mu\text{A} = 50 \times 10^{-6}\text{ A}\) Using Ohm's Law: \[ v_m = I_{fs} \cdot R_m = (50 \times 10^{-6}\text{ A}) \times 1000\ \Omega = 0.05\text{ V} \]

Step 2: Calculate the multiplication factor (\(m\)). The targeted new full scale voltage range \(V\) is 10 V. \[ m = \frac{V}{v_m} = \frac{10\text{ V}}{0.05\text{ V}} = 200 \]

Step 3: Compute the required series multiplier resistance value (\(R_{se}\)). Substitute the values into the multiplier formula: \[ R_{se} = R_m(m - 1) = 1\ \text{k}\Omega \times (200 - 1) \] \[ R_{se} = 1\ \text{k}\Omega \times 199 = 199\ \text{k}\Omega \] Thus, the value of the series resistance required is \(199\ \text{k}\Omega\), matching option (B).