What is the total current in a series circuit with a 10Ω resistor and a 20Ω indu

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Question: What is the total current in a series circuit with a 10Ω resistor and a 20Ω inductor connected to a 100V AC source at 50Hz? (2023)

Options:

Correct Answer: 4A

Exam Year: 2023

Solution:

Total impedance Z = √(R² + (ωL)²) = √(10² + (2π(50)(20))²). Calculate to find current.

What is the total current in a series circuit with a 10Ω resistor and a 20Ω inductor connected to a 100V AC source at 50Hz? (2023)

What is the total current in a series circuit with a 10Ω resistor and a 20Ω inductor connected to a 100V AC source at 50Hz? (2023)

Step 1: Identify the components in the circuit. We have a resistor (R) of 10Ω and an inductor (L) of 20Ω connected to a 100V AC source.
Step 2: Calculate the angular frequency (ω) using the formula ω = 2πf, where f is the frequency in Hz. Here, f = 50Hz, so ω = 2π(50).
Step 3: Calculate the inductive reactance (XL) using the formula XL = ωL. Substitute ω from Step 2 and L = 20Ω to find XL.
Step 4: Calculate the total impedance (Z) of the circuit using the formula Z = √(R² + (XL)²). Substitute R = 10Ω and XL from Step 3.
Step 5: Use Ohm's Law to find the total current (I) in the circuit using the formula I = V/Z, where V is the voltage (100V). Substitute V and Z from Step 4.

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