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

To convert the given voltmeter into an ammeter, we first determine the maximum current that flows through the voltmeter at its full-scale reading.

Step 1: Find the full-scale current of the voltmeter.
Given resistance of voltmeter, R_v = 300 Ω
Maximum voltage, V = 150 V

Using Ohm’s Law:
I_v = V / R_v
I_v = 150 / 300
I_v = 0.5 A

So, the voltmeter can carry a maximum current of 0.5 A safely.

Step 2: Determine the current through the shunt.
The ammeter is required to measure up to 8 A.
Current through shunt, I_s = Total current − Voltmeter current
I_s = 8 − 0.5
I_s = 7.5 A

Step 3: Calculate the shunt resistance.
Since the voltmeter and shunt are connected in parallel, the voltage across both is the same.

Voltage across voltmeter:
V = I_v × R_v
V = 0.5 × 300
V = 150 V

Shunt resistance, R_s = V / I_s
R_s = 150 / 7.5
R_s = 20 Ω

Final Answer:
The value of the required shunt resistance is 20 Ω.