A resistance `R` draws power `P` when connected to an `AC` source. If an inductance is now placed in series with the resistance, such that the impedence of the circuit becomes `Z`, the power drawn will be

Options

A. `P(R/Z)^(2)`
B. `Psqrt(R/Z)`
C. `P(R/Z)`
D. P

Explanation

To solve the problem step by step, we will analyze the power drawn by the resistance when connected to an AC source and how it changes when an inductance is added in series, affecting the impedance of the circuit.

### Step-by-Step Solution:

1. **Understanding Power in the Original Circuit:**
- When the resistance \( R \) is connected to an AC source, the power \( P \) drawn can be expressed using the formula:
\[ P = I_{\text{RMS}}^2 \cdot R \]
- Here, \( I_{\text{RMS}} \) is the root mean square current through the resistance.

2. **Finding the RMS Current:**
- The RMS current can be calculated as:
\[ I_{\text{RMS}} = \frac{V_{\text{RMS}}}{R} \]
- Substituting this into the power formula gives:
\[ P = \left(\frac{V_{\text{RMS}}}{R}\right)^2 \cdot R = \frac{V_{\text{RMS}}^2}{R} \]

3. **Introducing Inductance:**
- When an inductance is placed in series with the resistance, the total impedance \( Z \) of the circuit changes. The new power \( P' \) drawn from the AC source can be expressed as:
\[ P' = \frac{V_{\text{RMS}}^2}{Z} \cdot R \]

4. **Relating the New Power to the Original Power:**
- Now, we can relate the new power \( P' \) to the original power \( P \):
\[ P' = P \cdot \frac{R}{Z} \]
- To express this in terms of the original power \( P \), we can rewrite it as:
\[ P' = P \cdot \frac{R^2}{Z^2} \]

5. **Final Expression for Power:**
- Therefore, the new power drawn when the inductance is added in series is:
\[ P' = P \cdot \frac{R^2}{Z^2} \]

### Conclusion:
The power drawn when an inductance is placed in series with the resistance, affecting the impedance of the circuit, is given by:
\[ P' = P \cdot \frac{R^2}{Z^2} \]