A moving iron ammeter with a range of 0 to 1 amps has an inter... | General Science MCQ | Examoogle

General SciencePhysics: Electricity

A moving iron ammeter with a range of 0 to 1 amps has an internal resistance of 50 mΩ and an inductance of 0.1 MH. To increase the range to 0-10 Ampere for all operational frequencies, a shunt coil is connected. The shunt coils resistance in mΩ and time constant in milliseconds are each given as:

5.55, 2

2; 0.55

11.1; 2

2; 1

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity

Option A

55, 2

Quick Summary:

To extend the range of an ammeter for all frequencies (AC circuits), the shunt must have a time constant equal to that of the meter coil to ensure the division of current remains independent of frequency. This requires the ratio of inductance to resistance (L/R) to be identical for both the meter and the shunt.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of this as a 'current divider' bridge where both paths must react at the same speed to sudden changes, otherwise, the balance shifts when the signal frequency changes.

🔢 Key Formulas

$\frac{L_{m}}{R_{m}} = \frac{L_{s}}{R_{s}}$ — Time constant condition for AC shunts

$R_{s} = \frac{R_{m}}{n-1}$ — Shunt resistance formula where $n = \frac{I}{I_{m}}$

⚙️ Working Principle

For an ammeter of resistance $R_{m}$ and inductance $L_{m}$ , a shunt $R_{s}$ and $L_{s}$ is added. To maintain the same division ratio $n = \frac{I}{I_{m}} = 10$ across all frequencies, the condition $\frac{L_{m}}{R_{m}} = \frac{L_{s}}{R_{s}}$ must hold. Given $R_{m} = 50 \text{ m}\Omega$ and $L_{m} = 0.1 \text{ mH}$ , the shunt resistance is calculated as $R_{s} = \frac{R_{m}}{n-1} = \frac{50}{9} \approx 5.55 \text{ m}\Omega$ . The time constant is $\tau = \frac{L_{m}}{R_{m}} = \frac{0.1}{50} \text{ s} = 2 \text{ ms}$ .

📌 Key Points

▸
A shunt for DC meters only requires a resistor, but for AC, an inductor is necessary to match the time constant.
▸
Matching time constants ensures the multiplier is constant for all frequencies.
▸
The range extension factor $n$ is defined by the total current divided by the full-scale deflection current.

✅ Advantages

▸
Allows the same meter to measure higher current magnitudes.
▸
Ensures accuracy across varying power frequency inputs.

❌ Disadvantages / Limitations

▸
Requires precise impedance matching (L and R).
▸
Adding shunt components increases the physical size of the instrument circuitry.

🛠️ Applications / Uses

▸
Moving iron ammeter range extension.
▸
AC power measurement instrumentation.

📄 Additional Information

▸
The time constant $\tau$ is given by $\frac{L}{R}$ . Here $\frac{0.1 \times 10^{-3} \text{ H}}{50 \times 10^{-3} \text{ }\Omega} = 0.002 \text{ s} = 2 \text{ ms}$ .
▸
Option B, C, and D are incorrect because they fail to satisfy the ratio equality $\frac{L_{s}}{R_{s}} = \tau$ .

📊 Diagram / Illustration

✅

A is correct — The shunt resistance is $5.55 \text{ m}\Omega$ and the time constant is $2 \text{ ms}$ to maintain the frequency-independent current division.

Core Concepts Used

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Ammeter Shunt Time Constant Moving Iron Instrument

💡 EXAM TIP

Always check if the problem mentions 'AC' or 'all frequencies' when dealing with instrument shunts; if it does, you must match the inductive time constants, not just the resistive values.

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