An LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring mass damped oscillator having damping constant b, the correct equivalence of b would be:

Options

A. `b harr R`
B. `b harr c`
C. `b harr 1/R`
D. `b harr 1/L`

Explanation

To solve the problem of finding the equivalence of the damping constant \( b \) in an LCR circuit compared to a physical spring-mass damped oscillator, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Damped Harmonic Oscillator**:
- A damped harmonic oscillator can be described by the equation:
\[ m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = 0 \]
- Here, \( m \) is the mass, \( b \) is the damping constant, and \( k \) is the spring constant.

2. **Write the Equation for the LCR Circuit**:
- An LCR circuit consists of an inductor \( L \), a capacitor \( C \), and a resistor \( R \). The equation governing the current \( I \) in the circuit is:
\[ L \frac{d^2Q}{dt^2} + R \frac{dQ}{dt} + \frac{Q}{C} = 0 \]
- Here, \( Q \) is the charge on the capacitor.

3. **Identify the Corresponding Terms**:
- In the LCR circuit equation, the term \( R \frac{dQ}{dt} \) corresponds to the damping term in the mechanical oscillator equation. This is because both terms represent damping effects in their respective systems.

4. **Establish the Equivalence**:
- By comparing the coefficients of the first derivative terms in both equations, we can establish that:
\[ b \equiv R \]
- This means that the damping constant \( b \) in the mechanical oscillator is equivalent to the resistance \( R \) in the LCR circuit.

5. **Conclusion**:
- Therefore, the correct equivalence of the damping constant \( b \) for the LCR circuit is:
\[ b = R \]