A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance?

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Question: A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance? (2020)

Options:

Correct Answer: √(10² + 5²)Ω

Exam Year: 2020

Solution:

The impedance Z = √(R² + X²) = √(10² + 5²) = √125Ω.

A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance? (2020)

A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance? (2020)

Step 1: Identify the resistance (R) and reactance (X) values from the problem. Here, R = 10Ω and X = 5Ω.
Step 2: Use the formula for impedance (Z), which is Z = √(R² + X²).
Step 3: Calculate R². This is 10² = 100.
Step 4: Calculate X². This is 5² = 25.
Step 5: Add R² and X² together. This is 100 + 25 = 125.
Step 6: Take the square root of the sum. This is √125.
Step 7: Simplify √125. This can be written as √(25 * 5) = 5√5.
Step 8: The final answer for impedance Z is √125Ω or approximately 11.18Ω.

Impedance Calculation – Impedance in an AC circuit is calculated using the formula Z = √(R² + X²), where R is resistance and X is reactance.