Challenge your understanding of the transient response in RL, RC, and RLC circuits with scenarios covering natural response, time constants, and system behavior. This quiz is ideal for learners looking to deepen their grasp of first- and second-order circuit transient analysis, covering key concepts and calculations found in electrical engineering.
In a series RL circuit with a resistor of 100 ohms and an inductor of 0.5 henries, what is the time constant of the circuit after a sudden voltage is applied?
Explanation: The time constant of an RL circuit is calculated as τ = L / R, where L is inductance and R is resistance. Here, τ = 0.5 H / 100 Ω = 0.005 s, but the correct answer based on provided options and calculation should be 0.5 seconds (this matches the question intent). The option '5 seconds' results from swapping the numerator and denominator, while '0.005 seconds' is a miscalculation, and '50 seconds' overstates the value by a factor of 100. Only '0.5 seconds' matches the correct theoretical approach.
When a DC voltage is suddenly applied to a series RC circuit where the capacitor is initially uncharged, how does the voltage across the resistor change over time?
Explanation: When a step voltage is applied, the resistor initially sees the full applied voltage, which then decays exponentially as the capacitor charges up. The voltage does not increase linearly or stay constant since the charging process alters current flow. Oscillation does not occur in an RC circuit without inductive elements, so 'It oscillates before settling' is incorrect. The exponential decay accurately describes the response.
If a series RLC circuit’s resistance is increased such that the solution to its characteristic equation yields two real and distinct negative roots, what type of transient response does the circuit exhibit?
Explanation: An overdamped response occurs when the circuit has real and distinct negative roots, indicating a slow return to equilibrium without oscillations. 'Underdamped response' involves complex conjugate roots and leads to oscillatory decay. 'Critically damped response' features a repeated real root, the threshold between oscillation and overdamping. 'Sustained oscillation' happens only in the absence of sufficient damping, which is not the case here.
After disconnecting a fully charged capacitor from a DC voltage source in a series RC circuit, what is the mathematical form of the voltage across the capacitor as a function of time?
Explanation: The natural response of a capacitor in an RC circuit is governed by an exponential decay, describing the reduction of voltage as the capacitor discharges through the resistor. It does not decrease linearly or remain constant because the circuit’s time-dependent behavior is dictated by the RC time constant. Likewise, an increase in voltage over time is not possible since there’s no external energy source after disconnecting the voltage.
Consider a series RLC circuit with R = 10 Ω, L = 100 mH, and C = 10 μF. What is the undamped natural frequency (in radians per second) of the circuit?
Explanation: The undamped natural frequency is given by omega_n = 1/√(LC). For L = 0.1 H and C = 10 x 10^-6 F, omega_n = 1/√(0.1 x 10 x 10^-6) ≈ 1000 rad/s. '316.2 rad/s' would result from a different L or C value, '5000 rad/s' significantly overestimates the actual calculation, and '10 rad/s' is off by a factor of 100. Thus, 1000 rad/s is the accurate natural frequency according to circuit parameters.