In a parallel RLC circuit, if the resistance is 10Ω, inductance is 0.2H, and cap

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Question: In a parallel RLC circuit, if the resistance is 10Ω, inductance is 0.2H, and capacitance is 50μF, what is the total admittance? (2022)

Options:

Correct Answer: 0.3 S

Exam Year: 2022

Solution:

Total admittance Y = 1/R + j(ωC - 1/ωL). Calculate Y using given values.

In a parallel RLC circuit, if the resistance is 10Ω, inductance is 0.2H, and capacitance is 50μF, what is the total admittance? (2022)

In a parallel RLC circuit, if the resistance is 10Ω, inductance is 0.2H, and capacitance is 50μF, what is the total admittance? (2022)

Step 1: Identify the values given in the problem. Resistance (R) = 10Ω, Inductance (L) = 0.2H, Capacitance (C) = 50μF.
Step 2: Convert the capacitance from microfarads to farads. 50μF = 50 x 10^-6 F = 0.00005 F.
Step 3: Calculate the angular frequency (ω). If not given, assume a frequency (f) or use a standard frequency like 60Hz. For example, ω = 2πf = 2π(60) ≈ 376.99 rad/s.
Step 4: Calculate the capacitive reactance (X_C) using the formula X_C = 1/(ωC).
Step 5: Calculate the inductive reactance (X_L) using the formula X_L = ωL.
Step 6: Calculate the total admittance (Y) using the formula Y = 1/R + j(ωC - 1/ωL).
Step 7: Substitute the values into the formula and simplify to find the total admittance.

Admittance in RLC Circuits – Understanding how to calculate total admittance in a parallel RLC circuit using resistance, inductance, and capacitance.
Complex Numbers in Circuit Analysis – Applying complex numbers to represent the imaginary components of inductance and capacitance in admittance calculations.
Frequency Dependence – Recognizing that the total admittance depends on the angular frequency (ω), which is not provided in the question.