A resistor and a capacitor are connected to an ac supply of 200 V, 50 Hz, in series. The current in the circuit is 2A. If the power consumed in the circuit is 100 W then the resistance in the circuit is

Options

A. (A) `100 Omega`
B. (B) `25 Omega`
C. (C) `sqrt(125xx75)Omega`
D. (D) `400 Omega`

Explanation

To solve the problem step by step, we will use the given information about the AC circuit with a resistor and a capacitor.

### Step 1: Understand the Power Formula
In an AC circuit with a resistor and a capacitor in series, the power consumed (P) is given by the formula:
\[ P = I^2 R \]
where:
- \( P \) is the power consumed (in watts),
- \( I \) is the current (in amperes),
- \( R \) is the resistance (in ohms).

### Step 2: Identify Given Values
From the problem, we have:
- Power consumed, \( P = 100 \, \text{W} \)
- Current, \( I = 2 \, \text{A} \)

### Step 3: Rearrange the Power Formula
We need to find the resistance \( R \). Rearranging the power formula gives:
\[ R = \frac{P}{I^2} \]

### Step 4: Substitute the Values
Now, substitute the known values into the rearranged formula:
\[ R = \frac{100 \, \text{W}}{(2 \, \text{A})^2} \]

### Step 5: Calculate the Resistance
Calculating the denominator:
\[ (2 \, \text{A})^2 = 4 \, \text{A}^2 \]
Now substitute this back into the equation:
\[ R = \frac{100 \, \text{W}}{4 \, \text{A}^2} = 25 \, \Omega \]

### Conclusion
Thus, the resistance in the circuit is:
\[ R = 25 \, \Omega \]