In an experiment, 200V AC is applied at the end of an LCR circuit. The circuit consists of an inductive reactance
`(X_(L))` =`50Omega`, capacitive reactance
`(X_(c))=50Omega`, and capacitives resistance
`(R ) = 10Omega`, The impendance of the circuit is

Options

A. 1) `10Omega`
B. 2) `20Omega`
C. 3) `30Omega`
D. 4) `40Omega`

Answer

To find the impedance \( Z \) of the LCR circuit, we can use the following formula:

\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]

Where:
- \( R \) is the resistance,
- \( X_L \) is the inductive reactance,
- \( X_C \) is the capacitive reactance.

### Step 1: Identify the given values
From the question, we have:
- \( R = 10 \, \Omega \)
- \( X_L = 50 \, \Omega \)
- \( X_C = 50 \, \Omega \)

### Step 2: Calculate the difference between inductive and capacitive reactance
Next, we calculate \( X_L - X_C \):
\[ X_L - X_C = 50 \, \Omega - 50 \, \Omega = 0 \, \Omega \]

### Step 3: Substitute the values into the impedance formula
Now, substitute the values into the impedance formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{10^2 + 0^2} \]

### Step 4: Simplify the equation
This simplifies to:
\[ Z = \sqrt{100 + 0} = \sqrt{100} = 10 \, \Omega \]

### Step 5: Conclusion
Thus, the impedance \( Z \) of the circuit is:
\[ Z = 10 \, \Omega \]

### Final Answer
The impedance of the circuit is \( 10 \, \Omega \).

---