In a series combination of R, L and C to an A.C. Source at resonance if R = 200 hm, then impedance Z of the combination is

Options

A. 200 hm
B. zero
C. 10 hm
D. 4000 hm

Answer

To solve the problem of finding the impedance \( Z \) in a series combination of \( R \), \( L \), and \( C \) at resonance, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Resonance in RLC Circuit**:
- In a series RLC circuit, resonance occurs when the inductive reactance \( X_L \) is equal to the capacitive reactance \( X_C \). This means:
\[ X_L = X_C \]

2. **Impedance at Resonance**:
- At resonance, the total impedance \( Z \) of the circuit is purely resistive. This is because the reactive components (inductive and capacitive) cancel each other out. Therefore, the impedance can be expressed as:
\[ Z = R \]

3. **Given Values**:
- The problem states that the resistance \( R \) is given as \( 200 \, \Omega \).

4. **Calculating Impedance**:
- Since at resonance the impedance \( Z \) is equal to the resistance \( R \), we can conclude:
\[ Z = 200 \, \Omega \]

5. **Final Answer**:
- Thus, the impedance \( Z \) of the combination at resonance is:
\[ Z = 200 \, \Omega \]