Question

An ac voltage is applied to a resistance R and an inductor L in series. If R and the inductive reactance are both equal to 3Ω, the phase difference between the applied voltage and the current in the circuit is

• A. π/6
• B. π/4
• C. π/2
• D. zero

Hint:

The phase difference formula is used to determine the phase difference between the current and applied voltage.

Answer 1

The Correct Option is B

To find the phase difference between the applied voltage and the current in a circuit consisting of a resistor \( R \) and an inductor \( L \) in series, we need to use the concept of impedance in an AC circuit.

1. The impedance \( Z \) in a series R-L circuit is given by: Z = \sqrt{R^2 + X_L^2} where \( X_L \) is the inductive reactance.
2. Since both \( R \) and \( X_L \) are given as 3Ω, we can substitute these values into the equation: Z = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}\, \Omega
3. Next, in such a circuit, the phase difference (\( \phi \)) between the voltage and the current is given by: \tan \phi = \frac{X_L}{R} Substituting the given values: \tan \phi = \frac{3}{3} = 1
4. The angle whose tangent is 1 is \( \pi/4 \) radians or 45 degrees. Thus, the phase difference is: \phi = \pi/4

Therefore, the phase difference between the applied voltage and the current in the circuit is \( \pi/4 \).

Other option justifications:

• \pi/6, which equals approximately 30 degrees, applies when \( \tan \phi \approx 0.577 \), which is not the case here.
• \pi/2 radians, or 90 degrees, refers to a case where the impedance is entirely reactive, with no resistance.
• Zero phase difference occurs when there is only a resistive component present with no reactance.

Hence, the correct answer is \( \pi/4 \).