An ac ammeter is used to measure currnet in a circuit. When a given direct current passes through the circuit. The ac ammeter reads 3 A. When another alternating current passes through the circuit, the ac ammeter reads 4A. Then find the reading of this ammeter (inA), if dc and ac flow through the circuit simultaneously.

Options

A. 3A
B. 4A.
C. `7` A
D. 5A

Explanation

To solve the problem, we need to find the reading of the AC ammeter when both direct current (DC) and alternating current (AC) flow through the circuit simultaneously. We can use the principle of vector addition for currents, as DC and AC can be treated as perpendicular components in this case.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- The reading of the ammeter when only DC is present: \( I_{DC} = 3 \, \text{A} \)
- The reading of the ammeter when only AC is present: \( I_{AC} = 4 \, \text{A} \)

2. **Use the Formula for Total Current:**
When DC and AC are present simultaneously, the total current can be calculated using the Pythagorean theorem:
\[ I_{net} = \sqrt{I_{DC}^2 + I_{AC}^2} \]

3. **Substitute the Values:**
Substitute the values of \( I_{DC} \) and \( I_{AC} \) into the formula:
\[ I_{net} = \sqrt{3^2 + 4^2} \]

4. **Calculate the Squares:**
Calculate \( 3^2 \) and \( 4^2 \):
\[ 3^2 = 9 \quad \text{and} \quad 4^2 = 16 \]

5. **Add the Squares:**
Add the results:
\[ 9 + 16 = 25 \]

6. **Take the Square Root:**
Now take the square root of 25:
\[ I_{net} = \sqrt{25} = 5 \, \text{A} \]

7. **Final Result:**
Therefore, the reading of the ammeter when both DC and AC are flowing through the circuit simultaneously is:
\[ I_{net} = 5 \, \text{A} \]