Question

In an a.c. circuit, a resistance $R = 40\ \Omega$ and an inductance '$L$' are connected in series. If the phase angle between voltage and current is $45^\circ$, then the value of the inductive reactance is ($\tan 45^\circ = 1$)

• A. $50\ \Omega$
• B. $40\ \Omega$
• C. $10\ \Omega$
• D. $20\ \Omega$

Hint:

Whenever the phase angle in an alternating current circuit is exactly $45^\circ$, it means the adjacent component (resistance $R$) and the opposite component (reactance $X$) of the impedance triangle are completely identical in value. Therefore, you can instantly conclude $X_L = R = 40\ \Omega$ without doing any math!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question describes a series alternating current $RL$ circuit containing a resistor and an inductor. Given the total resistance and the angular phase shift angle between the voltage and current vectors, we need to solve for the inductive reactance ($X_L$).

Step 2: Key Formula or Approach:
In a series $RL$ circuit, the phase angle ($\phi$) between the total voltage and current phasor vectors is defined by the impedance triangle ratio: $$\tan\phi = \frac{X_L}{R}$$

Step 3: Detailed Explanation:
Let's list the values provided: Resistance, $R = 40\ \Omega$ Phase angle, $\phi = 45^\circ$ Substitute these values directly into our phase angle relationship formula: $$\tan(45^\circ) = \frac{X_L}{40}$$ Since $\tan 45^\circ = 1$: $$1 = \frac{X_L}{40} \implies X_L = 40\ \Omega$$

Step 4: Final Answer:
The inductive reactance of the circuit is $40\ \Omega$, matching option (B).