An inductive coil has a resistance of 100Ω. When an AC signal of frequency 1000Hz is fed to the coil the applied voltage leads the current by 45Ω. What is the inductance of the coil ?
Correct answer: C. 16mH
- A. 10mH
- B. 12mH
- C. 16mH
- D. 20mH
Explanation
A voltage-current phase angle of 45° gives tan 45° = XL/R = 1, so XL = 100 ohms. Then L = XL/(2πf) = 100 ohms/(2 x 3.14 x 1000 s^-1) = 0.0159 H = 15.9 mH, approximately 16 mH. Students may choose a or b by omitting the factor 2π or rounding too early.
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Alternating current through a resistor, capacitor and inductor involves phase relationships between voltage and current, reactance, impedance and energy transfer. A resistor keeps voltage and current in phase, while a capacitor and inductor produce opposite phase shifts, a distinction used in circuit diagrams and numerical calculations.
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