A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.

Explanation

To solve the problem step by step, we will calculate the impedance of the circuit and the time lag between the maximum alternating voltage and current.

### Step 1: Identify the Given Values
- Inductance (L) = 0.01 H
- Resistance (R) = 1 Ω
- Voltage (V) = 200 V (not needed for impedance calculation)
- Frequency (f) = 50 Hz

### Step 2: Calculate the Inductive Reactance (XL)
The inductive reactance (XL) can be calculated using the formula:
\[ X_L = 2 \pi f L \]
Substituting the values:
\[ X_L = 2 \pi (50) (0.01) = 2 \pi (0.5) = \pi \approx 3.14 \, \Omega \]

### Step 3: Calculate the Impedance (Z)
The impedance (Z) of an L-R circuit is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values of R and XL:
\[ Z = \sqrt{(1)^2 + (3.14)^2} = \sqrt{1 + 9.8596} = \sqrt{10.8596} \approx 3.30 \, \Omega \]

### Step 4: Calculate the Phase Difference (φ)
The phase difference (φ) can be calculated using:
\[ \tan \phi = \frac{X_L}{R} \]
Substituting the values:
\[ \tan \phi = \frac{3.14}{1} = 3.14 \]
Now, calculate φ:
\[ \phi = \tan^{-1}(3.14) \approx 72^\circ \]

### Step 5: Convert φ to Radians
To convert degrees to radians:
\[ \phi \text{ (in radians)} = \phi \times \frac{\pi}{180} = 72 \times \frac{\pi}{180} \approx 1.2566 \, \text{radians} \]

### Step 6: Calculate Angular Frequency (ω)
The angular frequency (ω) is given by:
\[ \omega = 2 \pi f \]
Substituting the value of f:
\[ \omega = 2 \pi (50) = 100 \pi \approx 314.16 \, \text{rad/s} \]

### Step 7: Calculate the Time Lag (Δt)
The time lag (Δt) can be calculated using:
\[ \Delta t = \frac{\phi}{\omega} \]
Substituting the values:
\[ \Delta t = \frac{1.2566}{314.16} \approx 0.004 \, \text{seconds} \quad \text{or} \quad \frac{1}{250} \, \text{seconds} \]

### Final Results
- Impedance (Z) = 3.30 Ω
- Time lag (Δt) = \( \frac{1}{250} \) seconds

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