A `40Omega` electric heater is connected to a 200 V , 50 Hz mains supply. The peak value of electric current flowing in the circuit is approximately

Options

A. 2.5 A
B. 5.0 A
C. `7 A`
D. `10 A`

Answer

To find the peak value of electric current flowing in the circuit, we will follow these steps:

### Step 1: Identify the given values
- Resistance of the electric heater (R) = 40 Ω
- RMS Voltage (V_RMS) = 200 V

### Step 2: Calculate the RMS current (I_RMS)
Using Ohm's Law, the RMS current can be calculated using the formula:
\[ I_{RMS} = \frac{V_{RMS}}{R} \]
Substituting the given values:
\[ I_{RMS} = \frac{200 \text{ V}}{40 \text{ Ω}} = 5 \text{ A} \]

### Step 3: Calculate the peak current (I_0)
The relationship between peak current (I_0) and RMS current (I_RMS) is given by:
\[ I_0 = \sqrt{2} \times I_{RMS} \]
Substituting the value of I_RMS:
\[ I_0 = \sqrt{2} \times 5 \text{ A} \]
Calculating this gives:
\[ I_0 \approx 1.414 \times 5 \approx 7.07 \text{ A} \]

### Step 4: Round off the peak current
Since the question asks for the approximate value:
\[ I_0 \approx 7 \text{ A} \]

### Final Answer
The peak value of electric current flowing in the circuit is approximately **7 A**.

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