A L-C-R circuit with L=1.00 mH, C=`10 muF` and `R=50Omega`, is driven with 5V AC voltage. At resonance, the current through the circuit is

Options

A. 0.2 A
B. 0.25 A
C. 0.15 A
D. 0.1 A

Explanation

To solve the problem, we need to find the current through an L-C-R circuit at resonance when given the values of inductance (L), capacitance (C), resistance (R), and the applied AC voltage (V).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Inductance, \( L = 1.00 \, \text{mH} = 1.00 \times 10^{-3} \, \text{H} \)
- Capacitance, \( C = 10 \, \mu\text{F} = 10 \times 10^{-6} \, \text{F} \)
- Resistance, \( R = 50 \, \Omega \)
- Voltage, \( V = 5 \, \text{V} \)

2. **Determine the Resonant Frequency:**
The resonant frequency \( f_0 \) for an L-C-R circuit is given by:
\[ f_0 = \frac{1}{2\pi \sqrt{LC}} \]
However, since we are only interested in the current at resonance, we can skip calculating \( f_0 \) directly.

3. **Calculate the Current at Resonance:**
At resonance, the current \( I \) through the circuit can be calculated using Ohm's Law:
\[ I = \frac{V}{R} \]
Substituting the known values:
\[ I = \frac{5 \, \text{V}}{50 \, \Omega} \]

4. **Perform the Calculation:**
\[ I = \frac{5}{50} = 0.1 \, \text{A} \]

5. **Conclusion:**
The current through the circuit at resonance is \( 0.1 \, \text{A} \).

### Final Answer:
The current through the circuit at resonance is **0.1 A**.