A dc ammeter and a hot wire ammeter are connected to a circuit in series. When a direct current is passed through circuit, the dc ammeter shows 6 A. When ac current flows through circuit, the ac ammeter shows 8A. What will be reading of each ammeter if dc and ac current flow simulataneously through the circuit?

Options

A. the DC ammeter will shown zero current
B. the DC ammeter will shown 6A current
C. the AC ammeter will shown 14A current
D. the AC ammeter will shown zero current

Answer

To solve the problem, we need to analyze the readings of the DC ammeter and the AC ammeter when both DC and AC currents flow simultaneously through the circuit. Let's break down the solution step by step.

### Step 1: Identify the given values
- The reading of the DC ammeter (I_DC) when only DC current flows is 6 A.
- The reading of the AC ammeter (I_AC) when only AC current flows is 8 A.

### Step 2: Understand the behavior of the ammeters
- The DC ammeter will continue to show the same reading (6 A) when DC current flows through the circuit.
- The reading of the AC ammeter when both currents flow simultaneously needs to be calculated.

### Step 3: Use the formula for power in terms of current
For the AC ammeter, the power can be expressed as:
\[ P = I^2 \cdot R \cdot t \]
Where:
- \( I \) is the current,
- \( R \) is the resistance,
- \( t \) is the time.

### Step 4: Set up the equation for simultaneous currents
When both DC and AC currents are flowing, the total power can be expressed as:
\[ P_{total} = P_{DC} + P_{AC} \]
This gives us:
\[ I^2_{total} \cdot R \cdot t = I^2_{DC} \cdot R \cdot t + I^2_{AC} \cdot R \cdot t \]

### Step 5: Simplify the equation
Since \( R \) and \( t \) are common in all terms, we can cancel them out:
\[ I^2_{total} = I^2_{DC} + I^2_{AC} \]

### Step 6: Substitute the known values
Now substituting the known values:
\[ I^2_{total} = (6)^2 + (8)^2 \]
\[ I^2_{total} = 36 + 64 \]
\[ I^2_{total} = 100 \]

### Step 7: Calculate the total current
Taking the square root to find the total current:
\[ I_{total} = \sqrt{100} = 10 \, A \]

### Step 8: Conclusion
- The reading of the DC ammeter remains 6 A.
- The effective reading of the AC ammeter when both currents flow simultaneously is 10 A.

### Final Answer:
- Reading of DC ammeter: **6 A**
- Reading of AC ammeter: **10 A**

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