An ac source of 220V, 40Hz is connected to pure inductor of inductance 0.01H and resistor of 6ohm in series. Calculate the time lag..... .. Ans : 0.01579 sec

To determine the time lag in an AC circuit consisting of a pure inductor and a resistor connected in series, we first need to understand the relationship between the voltage and current in such a circuit. The time lag, or phase difference, is influenced by the inductive reactance and the resistance in the circuit.

Understanding the Components

In this scenario, we have:

• AC Voltage Source: 220V
• Frequency (f): 40Hz
• Inductance (L): 0.01H
• Resistance (R): 6Ω

Calculating Inductive Reactance

The inductive reactance (X_L) can be calculated using the formula:

X_L = 2πfL

Substituting the values:

X_L = 2π(40)(0.01) = 2.51Ω

Finding the Impedance

The total impedance (Z) of the circuit is given by the formula:

Z = √(R² + X_L²)

Plugging in the values:

Z = √(6² + 2.51²) = √(36 + 6.3001) = √42.3001 ≈ 6.5Ω

Calculating the Phase Angle

The phase angle (φ) between the voltage and the current can be found using:

tan(φ) = X_L / R

Substituting the known values:

tan(φ) = 2.51 / 6

φ = arctan(2.51 / 6) ≈ 0.418 radians

Determining the Time Lag

The time lag (Δt) can be calculated from the phase angle using the formula:

Δt = φ / (2πf)

Substituting the values:

Δt = 0.418 / (2π(40))

Δt ≈ 0.01579 seconds

Final Thoughts

This time lag indicates how much the current lags behind the voltage in the circuit due to the inductive nature of the inductor. In practical terms, this means that when the voltage reaches its peak, the current will only reach its peak after approximately 0.01579 seconds. This concept is crucial in understanding how AC circuits behave, especially in applications involving inductors and resistors.