An A.C. voltage `V=5cos(1000t)V` is applied to an `L-R` series circuit of inductance 3 mH and resistance `4Omega`. The value of the maximum current in the circuit is ……………. A.

Answer

To find the maximum current in the given L-R series circuit with the applied AC voltage, we will follow these steps:

### Step 1: Identify the given values
- Voltage: \( V(t) = 5 \cos(1000t) \) V
- Inductance: \( L = 3 \, \text{mH} = 3 \times 10^{-3} \, \text{H} \)
- Resistance: \( R = 4 \, \Omega \)

### Step 2: Calculate the angular frequency (\( \omega \))
From the voltage equation, we can see that:
- \( \omega = 1000 \, \text{rad/s} \)

### Step 3: Calculate the inductive reactance (\( X_L \))
The inductive reactance is given by:
\[ X_L = \omega L \]
Substituting the values:
\[ X_L = 1000 \times 3 \times 10^{-3} = 3 \, \Omega \]

### Step 4: Calculate the total impedance (\( Z \))
The impedance in an L-R circuit is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values:
\[ Z = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \, \Omega \]

### Step 5: Calculate the maximum current (\( I_{max} \))
The maximum current can be calculated using Ohm's law for AC circuits:
\[ I_{max} = \frac{V_{max}}{Z} \]
Where \( V_{max} = 5 \, V \) (the coefficient of the cosine function). Thus:
\[ I_{max} = \frac{5}{5} = 1 \, \text{A} \]

### Final Answer
The maximum current in the circuit is \( 1 \, \text{A} \).

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