Question

A voltmeter of resistance \( 300\,\Omega \) measures up to \( 150\,\text{V} \). Find the value of the shunt required to convert it into an ammeter capable of measuring \( 8\,\text{A} \).

Hint:

To convert a voltmeter to an ammeter: Find voltmeter full-scale current first, then use parallel shunt formula \( R_s = \frac{V}{I - I_v} \).

Answer 1

Concept: To convert a voltmeter into an ammeter, a shunt resistance is connected in parallel. Key idea: 
Voltmeter full-scale current \( I_v = \frac{V}{R_v} \) 
Shunt carries remaining current 
Same voltage across voltmeter and shunt 
Step 1: Find full-scale current of voltmeter Given: \[ V = 150\,\text{V}, \quad R_v = 300\,\Omega \] \[ I_v = \frac{V}{R_v} = \frac{150}{300} = 0.5\,\text{A} \] So, voltmeter allows maximum current of \( 0.5\,\text{A} \). 
Step 2: Total current required Desired ammeter range: \[ I = 8\,\text{A} \] Current through shunt: \[ I_s = I - I_v = 8 - 0.5 = 7.5\,\text{A} \] Step 3: Voltage across shunt Voltage across voltmeter (and shunt in parallel): \[ V = I_v \times R_v = 0.5 \times 300 = 150\,\text{V} \] Step 4: Calculate shunt resistance \[ R_s = \frac{V}{I_s} = \frac{150}{7.5} = 20\,\Omega \] Final Answer: \[ \boxed{R_s = 20\,\Omega} \]