In a parallel RLC circuit, if R = 50 ohms, L = 0.2H, and C = 50μF, what is the t

₹0.0

Question: In a parallel RLC circuit, if R = 50 ohms, L = 0.2H, and C = 50μF, what is the total admittance? (2023)

Options:

Correct Answer: 0.06 S

Solution:

Y = 1/R + j(ωC - 1/ωL); calculate Y for given values.

In a parallel RLC circuit, if R = 50 ohms, L = 0.2H, and C = 50μF, what is the total admittance? (2023)

In a parallel RLC circuit, if R = 50 ohms, L = 0.2H, and C = 50μF, what is the total admittance? (2023)

Step 1: Identify the values given in the problem: R = 50 ohms, L = 0.2 H, C = 50 μF.
Step 2: Convert the capacitance from microfarads to farads: 50 μF = 50 x 10^-6 F.
Step 3: Calculate the angular frequency (ω) using the formula ω = 2πf, where f is the frequency. (Assume a frequency if not given, e.g., f = 60 Hz).
Step 4: Calculate the admittance due to resistance: Y_R = 1/R = 1/50 ohms.
Step 5: Calculate the admittance due to capacitance: Y_C = jωC.
Step 6: Calculate the admittance due to inductance: Y_L = -j(1/ωL).
Step 7: Combine the admittances: Total Admittance Y = Y_R + Y_C + Y_L.

Admittance in RLC Circuits – Understanding how to calculate total admittance in a parallel RLC circuit using the formula Y = 1/R + j(ωC - 1/ωL).
Complex Numbers in Circuit Analysis – Applying complex numbers to represent the reactive components (inductance and capacitance) in the admittance calculation.
Frequency Dependence – Recognizing that the total admittance depends on the angular frequency ω, which is not provided in the question.