Question

A micro-ammeter has a resistance of $100$ $\Omega$ and a full scale range of $50$ $\mu$ A. It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the current range and resistance combinations.

• A. 50 Volt range with 10 K$\Omega$ resitance in series
• B. 10 Volt range with 200K$\Omega$ resistance in series
• C. 5 mA range with 1 $\Omega$ resistance in parallel
• D. 10 mA range with 1 $\Omega$ resistance in parallel

Answer 1

Answer: (B), (C)

5 mA range with 1 $\Omega$ resistance in parallel
10 Volt range with 200K$\Omega$ resistance in series

Given the Microammeter has a resistance of 100 ohms and a full range of $50\mu$ amps

Ameter can function as a voltmeter when it is connected in series with a large resistance R. The value of R is determined by the maximum voltage that will be measured.

Checking for option A 50 V to produce a full-scale deflection of a voltmeter containing a 100- ammeter with a 50-A sensitivity. Then 50 V applied to the meter must produce a current of 50 A.

$R_{total}=R+r=\frac{V}{i}=\frac{50}{50\times {10}^{-6}}R\simeq 1000k\Omega$

Checking for option A 10 V to produce a full-scale deflection of a voltmeter containing a 100- ammeter with a 50-A sensitivity. Then 10 V applied to the meter must produce a current of 50 A.

$R_{total}=R+r=\frac{V}{i}=\frac{10}{50\times {10}^{-6}}R\simeq 200k\Omega$

Microammeter has a resistance of 100 ohms and a full range of $50\mu$ amps

Substituting them in the formula for shunt of Ammeter , we have

$S=\frac{G}{\frac{i}{i_g}-1}$

$S=\frac{100}{\frac{i}{50\times {10}^{-6}}-1}$

Option 2 and 3 has values of i and S that satisfy this equation.

Option B and C are correct