If both the resistance and the inductance in an LR AC series circuit are doubled the new impedance will be

Options

A. halved
B. fourfold
C. doubled
D. quadrupted

Explanation

To solve the problem, we need to determine the new impedance of an LR AC series circuit when both the resistance (R) and the inductance (L) are doubled.

### Step-by-Step Solution:

1. **Understand the Formula for Impedance**:
The impedance (Z) in an LR series circuit is given by the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]
where \(X_L\) (the inductive reactance) is given by:
\[ X_L = \omega L \]
Here, \(\omega\) is the angular frequency of the AC source.

2. **Identify the New Values**:
If both the resistance and the inductance are doubled, the new resistance (\(R'\)) and the new inductance (\(L'\)) can be expressed as:
\[ R' = 2R \]
\[ L' = 2L \]
Consequently, the new inductive reactance (\(X_L'\)) will be:
\[ X_L' = \omega L' = \omega (2L) = 2X_L \]

3. **Calculate the New Impedance**:
Substitute the new values into the impedance formula:
\[ Z' = \sqrt{(R')^2 + (X_L')^2} \]
This becomes:
\[ Z' = \sqrt{(2R)^2 + (2X_L)^2} \]
Simplifying this:
\[ Z' = \sqrt{4R^2 + 4X_L^2} \]
Factor out the common term:
\[ Z' = \sqrt{4(R^2 + X_L^2)} = 2\sqrt{R^2 + X_L^2} \]

4. **Relate New Impedance to Original Impedance**:
Recognizing that the original impedance \(Z\) is:
\[ Z = \sqrt{R^2 + X_L^2} \]
We can express the new impedance as:
\[ Z' = 2Z \]

5. **Conclusion**:
Therefore, the new impedance when both the resistance and the inductance are doubled is:
\[ Z' = 2Z \]

### Final Answer:
The new impedance will be doubled.