Current, Resistance and Ohm's Law - Exam Prep Insights

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Current, Resistance and Ohms Law - Transient Response in RC Circuits

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Current, Resistance and Ohms Law - Transient Response in RC Circuits MCQ & Objective Questions

The topic of "Current, Resistance and Ohms Law - Transient Response in RC Circuits" is crucial for students preparing for various school and competitive exams. Understanding these concepts not only helps in grasping the fundamentals of electrical circuits but also enhances problem-solving skills. Practicing MCQs and objective questions on this topic is essential for effective exam preparation, as it allows students to familiarize themselves with important questions and boosts their confidence.

What You Will Practise Here

Fundamental concepts of current, resistance, and Ohm's Law
Understanding transient response in RC circuits
Key formulas related to charging and discharging of capacitors
Time constant and its significance in circuit analysis
Graphical representation of voltage and current in RC circuits
Applications of RC circuits in real-world scenarios
Common circuit configurations and their analysis

Exam Relevance

This topic is frequently featured in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that test their understanding of Ohm's Law, the behavior of circuits during transient states, and the application of relevant formulas. Common question patterns include numerical problems, conceptual questions, and diagram-based queries that require a clear understanding of the transient response in RC circuits.

Common Mistakes Students Make

Confusing the time constant with other circuit parameters
Misapplying Ohm's Law in transient scenarios
Overlooking the significance of initial and final conditions in RC circuits
Failing to interpret graphs correctly during analysis

FAQs

Question: What is the time constant in an RC circuit?
Answer: The time constant (τ) is the product of resistance (R) and capacitance (C), represented as τ = R × C. It indicates the time taken for the voltage across the capacitor to reach approximately 63.2% of its final value during charging.

Question: How does the transient response affect circuit performance?
Answer: The transient response determines how quickly a circuit responds to changes in voltage or current, which is critical for timing applications and signal processing.

We encourage you to solve practice MCQs and test your understanding of "Current, Resistance and Ohms Law - Transient Response in RC Circuits". This will not only prepare you for exams but also solidify your grasp of essential concepts. Start practicing today and enhance your exam readiness!

Q. If a capacitor discharges through a resistor, what is the formula for the voltage across the capacitor at time t?

A. V(t) = V0 * e^(-t/RC)
B. V(t) = V0 * (1 - e^(-t/RC))
C. V(t) = V0 * t/RC
D. V(t) = V0 * e^(t/RC)

Solution

The voltage across a discharging capacitor is given by V(t) = V0 * e^(-t/RC).

Correct Answer: A — V(t) = V0 * e^(-t/RC)

Q. If a resistor of 10 ohms and a capacitor of 100 microfarads are in series, what is the time constant of the circuit?

A. 0.001 seconds
B. 0.01 seconds
C. 1 second
D. 0.1 seconds

Solution

The time constant τ = R * C = 10 ohms * 100 x 10^-6 F = 0.001 seconds or 1 millisecond.

Correct Answer: B — 0.01 seconds

Q. If the capacitance in an RC circuit is doubled, what happens to the time constant?

A. It remains the same.
B. It doubles.
C. It halves.
D. It quadruples.

Solution

Doubling the capacitance in an RC circuit will double the time constant τ = R * C.

Correct Answer: B — It doubles.

Q. In a parallel RC circuit, what happens to the total current as the capacitor charges?

A. It increases.
B. It decreases.
C. It remains constant.
D. It oscillates.

Solution

As the capacitor charges, the current through the capacitor decreases, leading to a decrease in total current.

Correct Answer: B — It decreases.

Q. In a series RC circuit, if the resistance is doubled, how does the time constant change?

A. It remains the same.
B. It doubles.
C. It halves.
D. It quadruples.

Solution

The time constant τ = R * C, so if R is doubled, τ also doubles.

Correct Answer: B — It doubles.

Q. In a series RC circuit, if the resistance is doubled, what happens to the time constant?

A. It remains the same.
B. It doubles.
C. It halves.
D. It quadruples.

Solution

The time constant τ = R * C will double if the resistance R is doubled, assuming capacitance C remains constant.

Correct Answer: B — It doubles.

Q. In an RC circuit, if the capacitor is fully charged, what is the current through the circuit?

A. Maximum current
B. Zero current
C. Current equals voltage
D. Current equals resistance

Solution

When the capacitor is fully charged, the current through the circuit is zero because the capacitor blocks any further current flow.

Correct Answer: B — Zero current

Q. In an RC circuit, what happens to the current as time approaches infinity after the switch is closed?

A. It approaches zero.
B. It approaches the maximum value V/R.
C. It oscillates indefinitely.
D. It becomes negative.

Solution

As time approaches infinity, the capacitor becomes fully charged and the current approaches the maximum value V/R, where V is the voltage and R is the resistance.

Correct Answer: B — It approaches the maximum value V/R.

Q. In an RC circuit, what happens to the voltage across the capacitor as time approaches infinity after a switch is closed?

A. It remains zero.
B. It equals the supply voltage.
C. It oscillates.
D. It becomes negative.

Solution

As time approaches infinity, the capacitor charges to the supply voltage, so the voltage across it equals the supply voltage.

Correct Answer: B — It equals the supply voltage.

Q. What is the final charge (Q) on a capacitor in an RC circuit when a voltage (V) is applied?

A. Q = CV
B. Q = V/R
C. Q = V^2/R
D. Q = I * t

Solution

The final charge on a capacitor when a voltage V is applied is given by Q = CV, where C is the capacitance.

Correct Answer: A — Q = CV

Q. What is the final charge on a capacitor (Q) in an RC circuit after a long time if the voltage across it is 5V and the capacitance is 200 microfarads?

A. 0.001 C
B. 0.01 C
C. 0.0001 C
D. 0.1 C

Solution

The charge Q is given by Q = C * V = 200 x 10^-6 F * 5 V = 0.001 C.

Correct Answer: A — 0.001 C

Q. What is the final voltage across the capacitor in a charging RC circuit if the applied voltage is 12V?

A. 0V
B. 6V
C. 12V
D. 24V

Solution

The final voltage across the capacitor in a charging RC circuit will equal the applied voltage, which is 12V.

Correct Answer: C — 12V

Q. What is the formula for calculating the current (I) in an RC circuit after a time (t) when a voltage (V) is applied?

A. I = V/R
B. I = V(1 - e^(-t/RC))
C. I = V/R * e^(-t/RC)
D. I = V * e^(-t/RC)

Solution

The current in an RC circuit after a time t is given by I = V(1 - e^(-t/RC)), where V is the voltage, R is the resistance, and C is the capacitance.

Correct Answer: B — I = V(1 - e^(-t/RC))

Q. What is the relationship between voltage, current, and resistance in an RC circuit according to Ohm's Law?

A. V = I * R
B. I = V * R
C. R = V/I
D. Both A and C

Solution

According to Ohm's Law, the relationship is V = I * R and R = V/I, so both A and C are correct.

Correct Answer: D — Both A and C

Q. What is the time constant (τ) in an RC circuit?

A. τ = R + C
B. τ = R * C
C. τ = R/C
D. τ = 1/(R*C)

Solution

The time constant τ in an RC circuit is given by τ = R * C, where R is the resistance and C is the capacitance.

Correct Answer: B — τ = R * C

Q. What is the time constant (τ) of an RC circuit?

A. R * C
B. R + C
C. R / C
D. 1 / (R * C)

Solution

The time constant τ of an RC circuit is given by the product of resistance and capacitance, τ = R * C.

Correct Answer: A — R * C

Q. What is the voltage across a capacitor after one time constant in an RC charging circuit?

A. 63.2% of the supply voltage
B. 50% of the supply voltage
C. 100% of the supply voltage
D. 36.8% of the supply voltage

Solution

After one time constant, the voltage across the capacitor reaches approximately 63.2% of the supply voltage.

Correct Answer: A — 63.2% of the supply voltage

Q. What is the voltage across the capacitor after one time constant in an RC charging circuit?

A. V(1 - e^(-1))
B. V(1 + e^(-1))
C. V/e
D. V

Solution

After one time constant, the voltage across the capacitor is V(1 - e^(-1)), where V is the applied voltage.

Correct Answer: A — V(1 - e^(-1))

Q. What is the voltage across the capacitor in an RC circuit after one time constant?

A. 0.63V
B. 0.37V
C. 1.0V
D. 0.5V

Solution

After one time constant (τ), the voltage across the capacitor reaches approximately 63% of the applied voltage V.

Correct Answer: A — 0.63V

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