A circuit contains an ammeter, a battery of `30 V` and a resistance `40.8 ohm` all connected in series. If the ammeter has a coil of resistance `480 ohm` and a shunt of `20 ohm`, the reading in the ammeter will be

Options

A. `1 A`
B. `0.5 A`
C. `0.25 A`
D. `2 A`

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Circuit Configuration
We have a circuit consisting of:
- A battery of 30 V
- A resistor of 40.8 ohms
- An ammeter with an internal resistance of 480 ohms and a shunt resistance of 20 ohms.

### Step 2: Identify the Total Resistance in the Circuit
The ammeter has a coil resistance of 480 ohms and a shunt of 20 ohms. Since the shunt is connected in parallel with the coil, we need to find the equivalent resistance of the ammeter.

The formula for the equivalent resistance \( R_{shunt} \) of two resistors in parallel \( R_1 \) and \( R_2 \) is given by:

\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]

Here, \( R_1 = 480 \, \text{ohm} \) (coil resistance) and \( R_2 = 20 \, \text{ohm} \) (shunt resistance).

Calculating \( R_{eq} \):

\[ \frac{1}{R_{eq}} = \frac{1}{480} + \frac{1}{20} \]

Calculating the right-hand side:

\[ \frac{1}{R_{eq}} = \frac{1}{480} + \frac{24}{480} = \frac{25}{480} \]

Thus,

\[ R_{eq} = \frac{480}{25} = 19.2 \, \text{ohm} \]

### Step 3: Calculate Total Resistance in the Circuit
Now, we need to find the total resistance in the circuit, which is the sum of the external resistor and the equivalent resistance of the ammeter:

\[ R_{total} = R_{external} + R_{eq} = 40.8 \, \text{ohm} + 19.2 \, \text{ohm} = 60 \, \text{ohm} \]

### Step 4: Calculate the Total Current in the Circuit
Using Ohm's Law, we can find the total current \( I \) flowing through the circuit. Ohm's Law states:

\[ I = \frac{V}{R} \]

Substituting the values:

\[ I = \frac{30 \, \text{V}}{60 \, \text{ohm}} = 0.5 \, \text{A} \]

### Step 5: Conclusion
The reading in the ammeter will be \( 0.5 \, \text{A} \).

### Final Answer
The reading in the ammeter is **0.5 A**.

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