Question

In a series LCR Circuit R = 300 Ω, L = 0.9 H, c = 2.0 µF and w = 1000 rad/sec. Then the impedance of the circuit is

• A. 500 Ω
• B. 1300 Ω
• C. 400 Ω
• D. 900 Ω

Answer 1

Answer: (A)

500 Ω

Answer 2

The impedance of a series LCR circuit can be calculated using the formula:
Z = √(R2 + (XL - XC)2)
where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
Given values:
R = 300 Ω
L = 0.9 H
C = 2.0 µF
ω = 1000 rad/sec
The inductive reactance (XL) can be calculated as follows:
XL = ωL
Substituting the given values:
XL = (1000 rad/sec)(0.9 H) = 900 Ω
The capacitive reactance (XC) can be calculated as follows:
XC = 1 / (ωC)
Substituting the given values:
XC = 1 / ((1000 rad/sec)(2.0 µF)) = 1 / (2 × 10-6) / 1000 = 500 Ω
Now we can substitute the values of R, XL, and XC into the impedance formula:
Z = √(3002 + (900 - 500)2) = √(90000 + 160000) = √(250000) = 500 Ω
Therefore, the impedance of the circuit is 500 Ω. So the correct option is (A) 500 Ω.