A series LCR circuit consists of R = 80, XL = 100, and XC = 40. The input voltage is 2500 (100 t) V. The amplitude of current, in the circuit, is........ A.

Given: R = 80, XL = 100, XC = 40, and voltage amplitude V = 2500 V. Find: The amplitude of current in the series LCR circuit. For a series LCR circuit, the total impedance is Z = R^2 + (XL - XC)^2 Substituting the given values, Z = 80^2 + (100 - 40)^2 Z = 6400 + 3600 = 10000 = 100 Now, the current amplitude is I = VZ = 2500100 = 25 A Therefore, the amplitude of current is 25 A.

A series LCR circuit consists of R = 80, XL = 100, and XC = 40. T… — Solution | JEE Physics

NVAEasyJEE 2023LCR Circuits & Resonance

A series LCR circuit consists of $R = 80 \, \Omega$ , $X_L = 100 \, \Omega$ , and $X_C = 40 \, \Omega$ . The input voltage is $2500 \cos(100 \pi t)$ V. The amplitude of current, in the circuit, is ........ A.

Answer

Correct answer:25

Step-by-step solution

Standard Method

Given: $R = 80 \, \Omega$ , $X_L = 100 \, \Omega$ , $X_C = 40 \, \Omega$ , and voltage amplitude $V = 2500 \, \text{V}$ .

Find: The amplitude of current in the series LCR circuit.

For a series LCR circuit, the total impedance is

Z = \sqrt{R^2 + (X_L - X_C)^2}

Substituting the given values,

Z = \sqrt{80^2 + (100 - 40)^2}

Z = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \, \Omega

Now, the current amplitude is

I = \frac{V}{Z} = \frac{2500}{100} = 25 \, \text{A}

Therefore, the amplitude of current is $25 \, \text{A}$ .

Common mistakes

Using $R + X_L + X_C$ directly as impedance is incorrect because resistance and net reactance combine through the impedance relation. Use $Z = \sqrt{R^2 + (X_L - X_C)^2}$ instead.
Adding $X_L$ and $X_C$ instead of taking their difference is wrong in a series LCR circuit. The net reactance is $X_L - X_C$ , not $X_L + X_C$ .
Using RMS voltage instead of amplitude causes an incorrect current value. Here, the source is written as $2500 \cos(100 \pi t)$ , so the voltage amplitude is $2500 \, \text{V}$ .

Practice more LCR Circuits & Resonance questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trial More on LCR Circuits & Resonance

Answer

Step-by-step solution

Common mistakes

Practice more LCR Circuits & Resonance questions

Related questions