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

Explanation

To find the resistance in the circuit, we can use the information provided in the question. Here’s a step-by-step solution:

### Step 1: Write down the given values
- Voltage (V) = 200 V
- Frequency (f) = 50 Hz
- Current (I) = 2 A
- Power (P) = 100 W

### Step 2: Understand the relationship between power, current, and resistance
In an AC circuit, the power consumed can be expressed using 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 3: Rearrange the formula to find resistance
We can rearrange the formula to solve for resistance \( R \):
\[ R = \frac{P}{I^2} \]

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

### Step 5: Calculate the value of resistance
Calculate \( I^2 \):
\[ I^2 = 2^2 = 4 \]
Now substitute this value back into the equation for \( R \):
\[ R = \frac{100}{4} = 25 \, \Omega \]

### Conclusion
The resistance in the circuit is \( 25 \, \Omega \).

---