A series LCR circuit is connected to an alternating source of emf . The current amplitude at resonance frequency is . If the value of resistance becomes twice of its initial value, then amplitude of current at resonance will be:
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Official Solution
Correct Option: (1)
In an LCR circuit, the current amplitude at resonance is given by: where is the resistance, is the emf, and is the total resistance in the circuit. If the resistance is doubled, the current will decrease as the current is inversely proportional to the resistance. Therefore, if the resistance becomes twice the initial value, the current will be half of its initial value: Thus, the correct answer is .
02
PYQ 2025
hard
physicsID: jee-main
For the AC circuit shown in the figure, and , and the phase difference between and is 90°. The input signal frequency is rad/sec, where is:
Official Solution
Correct Option: (1)
We are given that: The phase difference between and is 90°. The phase difference in a series RC circuit is given by: Given that , we have: This implies: Where: is the angular frequency (in rad/sec) Substituting these values into the equation: Simplifying: The angular frequency is related to the frequency by: Thus: Solving for : We are asked to express the frequency in the form : Therefore, . % Final Answer
x = 5
03
PYQ 2025
easy
physicsID: jee-main
An electric bulb rated as 100 W-220 V is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is :
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0.64 A
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0.45 A
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2.2 A
4
0.32 A
Official Solution
Correct Option: (1)
We need to find the peak value of current through a bulb rated at 100 W when connected to an AC source of 220 V.
The given details are as follows:
Power (P) = 100 W
RMS Voltage (Vrms) = 220 V
First, we need to find the resistance (R) of the bulb. For an electric bulb, the power (P) is related to the voltage (Vrms) and resistance (R) by the formula:
Rearranging this formula to find R, we have:
Substitute the values:
Next, we find the RMS current (Irms) using Ohm's Law:
Substitute the values:
The peak current (Ipeak) is related to the RMS current by the formula:
Substitute the value of Irms:
Thus, the peak value of current through the bulb is approximately 0.64 A.
Therefore, the correct answer is 0.64 A.
04
PYQ 2025
easy
physicsID: jee-main
An AC current is represented as:The RMS value of the current is:
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50 Amp
2
100 Amp
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10 Amp
4
Amp
Official Solution
Correct Option: (3)
Step 1: Identify Current Components The given current consists of:
A DC component: Amp (constant term)
An AC component: Amp
Step 2: RMS Value of AC Component For any sinusoidal current , the RMS value is: Here, Amp, so: Step 3: Total RMS Value Calculation When both DC and AC components are present: Substituting the values: Verification
Sum of squares:
Common Mistakes to Avoid
Ignoring the DC component's contribution
Forgetting to divide the peak value by for AC RMS
Adding RMS values directly instead of their squares
Conclusion The correct RMS value of the current is 3 (10 Amp).
05
PYQ 2025
medium
physicsID: jee-main
An alternating current is represented by the equation, ampere. The RMS value of current and the frequency of the given alternating current are
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Official Solution
Correct Option: (3)
1. RMS value of current: 2. Frequency of the current: Therefore, the correct answer is (3) .
06
PYQ 2026
medium
physicsID: jee-main
An inductor of 10 mH, capacitor of 0.1 µF and a resistor of 100 Ω are connected in series across an a.c power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitance reactance is Ω. The value of is ______.
Official Solution
Correct Option: (1)
Step 1: Understanding the Concept:
In an LCR series circuit, the power factor is defined as , where is the total impedance. The impedance is given by .
Step 2: Key Formula or Approach:
1. Power Factor
2.
3. Reactance difference
Step 3: Detailed Explanation:
1. Since , we have .
2. Substitute into the impedance formula:
3. Taking the square root:
4. Given :
5. Comparing with the given form :
Step 4: Final Answer:
The value of is 100.
07
PYQ 2026
medium
physicsID: jee-main
A series LCR circuit with is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _____ .
Official Solution
Correct Option: (1)
Step 1: Understanding the Concept:
Resonance in a series LCR circuit occurs when the inductive reactance ( ) and capacitive reactance ( ) become equal. At this state, the angular frequency is called the resonant frequency. : Key Formula or Approach:
Resonant frequency .
Inductive Reactance . Step 2: Detailed Explanation:
Given:
.
.
Calculate resonant angular frequency :
.
Calculate inductive reactance :
. Step 3: Final Answer:
The inductive reactance at resonant frequency is 200 .
08
PYQ 2026
medium
physicsID: jee-main
The figure given below shows an LCR series circuit with two switches and . When switch is closed keeping open, the phase difference between the current and source voltage is 30° and phase difference is 60° when is closed keeping open. The value of is _______ H.}
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3
Official Solution
Correct Option: (1)
Step 1: Understanding the given circuit.
In the LCR circuit, the phase difference between the current and the voltage is given by:
where is the inductive reactance, is the capacitive reactance, and is the resistance. Step 2: Phase difference with different conditions.
- When is closed and is open, the inductance is in the circuit. The phase difference is 30°, so:
- When is closed and is open, the inductance is in the circuit. The phase difference is 60°, so:
Step 3: Solving for .
By using the relationships for and simplifying the given equations, we find that the value of is H. Final Answer: (A)
09
PYQ 2026
medium
physicsID: jee-main
An a.c. source of angular frequency is connected across a resistor and a capacitor in series. The current is observed as . Now the frequency of the source is changed to , (keeping the voltage unchanged) the current is found to be . The ratio of resistance to reactance at frequency is:
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Official Solution
Correct Option: (3)
Step 1: Understanding the Question: We need to set up equations for current in an RC circuit at two different frequencies and solve for the ratio . Step 2: Key Formula or Approach: 1. . 2. Impedance . 3. Capacitive reactance . Step 3: Detailed Explanation: Case 1: At frequency . ...(1) Case 2: At frequency . New reactance . Current ...(2) Divide (1) by (2):
Step 4: Final Answer: The ratio is .
10
PYQ 2026
medium
physicsID: jee-main
In the given circuit, energy stored in the inductor is and power dissipated in resistance is . Find the value of .
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Official Solution
Correct Option: (1)
Concept:
For an AC circuit containing an inductor and a resistor:
Average energy stored in an inductor: Power dissipated in a resistor: Inductive reactance:
Step 1: Use Energy Stored in Inductor Given:
Step 2: Use Power Dissipated in Resistance Given:
Step 3: Find Inductance Substitute (2) into (1):
Step 4: Calculate Given frequency:
