Which of the following parameter in the series LCR circuit is analogous to driving force F(t) in mechanics :-

Options

A. Current dq/dt, here q is the charge
B. Inductance L
C. Capacitance C
D. Voltage ‘e’

Answer

To solve the question, we need to identify which parameter in a series LCR circuit is analogous to the driving force \( F(t) \) in mechanics.

### Step-by-Step Solution:

1. **Understand the Context**: In mechanics, the driving force \( F(t) \) is responsible for causing motion. Similarly, in an electrical circuit, we have parameters that drive the current through the circuit.

2. **Recall the Equations**:
- In mechanics, the equation for forced oscillation can be written as:
\[ m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = F(t) \]
where \( m \) is mass, \( b \) is damping coefficient, \( k \) is spring constant, and \( F(t) \) is the driving force.
- In a series LCR circuit, the analogous equation can be expressed as:
\[ L \frac{d^2Q}{dt^2} + R \frac{dQ}{dt} + \frac{Q}{C} = E(t) \]
where \( L \) is inductance, \( R \) is resistance, \( C \) is capacitance, \( Q \) is charge, and \( E(t) \) is the voltage (or electromotive force).

3. **Identify the Analogous Terms**:
- In the mechanical equation, the term \( F(t) \) is the driving force.
- In the electrical equation, the term \( E(t) \) represents the voltage that drives the current through the circuit.

4. **Conclusion**: By comparing the two equations, we can see that the driving force \( F(t) \) in mechanics is analogous to the voltage \( E(t) \) in the series LCR circuit.

5. **Select the Correct Option**: From the given options, the parameter that is analogous to the driving force \( F(t) \) is the voltage \( E \).

### Final Answer:
The parameter in the series LCR circuit that is analogous to the driving force \( F(t) \) in mechanics is **voltage \( E \)** (Option 4).

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