If frequency of R- L circuit is f then impedence will be

Options

A. `sqrt(R^2+(2pifL)^2)`
B. `R^2+ (2pif^2)^2`
C. `sqrt(R^Lpif^2)`
D. `sqrt((R^2 - Lpif^2))`

Explanation

To find the impedance of an R-L circuit given the frequency \( f \), we can follow these steps:

### Step 1: Understand the Formula for Impedance
The impedance \( Z \) of an R-L circuit is given by the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]
where \( R \) is the resistance and \( X_L \) is the inductive reactance.

### Step 2: Determine the Inductive Reactance
The inductive reactance \( X_L \) is defined as:
\[ X_L = \omega L \]
where \( \omega \) is the angular frequency. The angular frequency \( \omega \) is related to the frequency \( f \) by the equation:
\[ \omega = 2\pi f \]
Thus, we can express \( X_L \) in terms of \( f \):
\[ X_L = 2\pi f L \]

### Step 3: Substitute \( X_L \) into the Impedance Formula
Now, substitute \( X_L \) back into the impedance formula:
\[ Z = \sqrt{R^2 + (2\pi f L)^2} \]

### Step 4: Simplify the Expression
This gives us the final expression for the impedance of the R-L circuit:
\[ Z = \sqrt{R^2 + (2\pi f L)^2} \]

### Conclusion
Thus, the impedance \( Z \) of the R-L circuit at frequency \( f \) is:
\[ Z = \sqrt{R^2 + (2\pi f L)^2} \]

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