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In an AC circuit, the power factor...

In an `AC` circuit, the power factor

A

is zero when the circuit contain an ideal resistance only

B

is unity when the circuit contains an ideal resistance only

C

is zero when the circuit contains an ideal inductance only

D

is unity when the circuit contains an ideal inductance only

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The correct Answer is:
To solve the question regarding the power factor in an AC circuit, we will analyze the provided options step by step. ### Step 1: Understand the Power Factor The power factor (PF) in an AC circuit is defined as: \[ \text{Power Factor} = \cos \phi \] where \( \phi \) is the phase angle between the voltage and current. It can also be expressed in terms of resistance (R) and reactance (X): \[ \text{Power Factor} = \frac{R}{\sqrt{R^2 + (X_L - X_C)^2}} \] ### Step 2: Analyze Each Option Let's evaluate the options given in the question. #### Option A: Power factor is zero when the circuit contains ideal resistance only. - If the circuit contains only ideal resistance, then \( X_L = 0 \) and \( X_C = 0 \). - Thus, the power factor becomes: \[ \text{PF} = \frac{R}{\sqrt{R^2}} = \frac{R}{R} = 1 \] - Therefore, this statement is **incorrect**. #### Option B: Power factor is unity when the circuit contains ideal resistance only. - As calculated above, when the circuit contains only resistance, the power factor is indeed: \[ \text{PF} = 1 \] - Therefore, this statement is **correct**. #### Option C: Power factor is 0 when the circuit contains ideal inductance only. - If the circuit contains only an ideal inductor, then \( R = 0 \) and \( X_C = 0 \). - The power factor becomes: \[ \text{PF} = \frac{0}{\sqrt{0^2 + X_L^2}} = 0 \] - Therefore, this statement is **correct**. #### Option D: Power factor is unity when there is ideal inductance only. - For an ideal inductor, the power factor is: \[ \text{PF} = 0 \] - Therefore, this statement is **incorrect**. ### Conclusion From the analysis: - Correct options are: **B and C**. - Incorrect options are: **A and D**. ### Final Answer The correct options regarding the power factor in an AC circuit are **B and C**. ---
To solve the question regarding the power factor in an AC circuit, we will analyze the provided options step by step. ### Step 1: Understand the Power Factor The power factor (PF) in an AC circuit is defined as: \[ \text{Power Factor} = \cos \phi \] where \( \phi \) is the phase angle between the voltage and current. It can also be expressed in terms of resistance (R) and reactance (X): \[ \text{Power Factor} = \frac{R}{\sqrt{R^2 + (X_L - X_C)^2}} \] ...
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