A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?
Practice Questions
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Q1
A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?
1 kHz
10 kHz
100 Hz
1000 Hz
Capacitive reactance (X_C) is given by X_C = 1 / (2πfC). Rearranging gives f = 1 / (2πX_CC). Substituting X_C = 50 ohms and C = 10 x 10^-6 F gives f = 318.31 Hz, approximately 1 kHz.
Questions & Step-by-step Solutions
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Q
Q: A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?
Solution: Capacitive reactance (X_C) is given by X_C = 1 / (2πfC). Rearranging gives f = 1 / (2πX_CC). Substituting X_C = 50 ohms and C = 10 x 10^-6 F gives f = 318.31 Hz, approximately 1 kHz.
Steps: 7
Step 1: Understand the formula for capacitive reactance, which is X_C = 1 / (2πfC).
Step 2: Identify the values given in the problem: X_C = 50 ohms and C = 10 microfarads (which is 10 x 10^-6 farads).
Step 3: Rearrange the formula to solve for frequency (f): f = 1 / (2πX_CC).
Step 4: Substitute the values into the rearranged formula: f = 1 / (2π * 50 * 10 x 10^-6).
Step 5: Calculate the denominator: 2π * 50 * 10 x 10^-6 = 0.00314.
Step 6: Calculate the frequency: f = 1 / 0.00314 = 318.31 Hz.
Step 7: Round the answer to the nearest kilohertz: approximately 1 kHz.
