Analog VLSI Basics: Passive Circuits and First-Order RC/RL Questions Quiz

Explore essential concepts in analog VLSI with a focus on passive circuits and the behavior of first-order RC and RL circuits. This quiz aims to enhance understanding of time constants, transient responses, filtering properties, and the roles of resistors, capacitors, and inductors in basic circuits.

1. RC Circuit Time Constant Identification

   What is the time constant (tau) of an RC circuit consisting of a 2 kΩ resistor and a 5 μF capacitor connected in series?

   1. 10 seconds
   2. 0.01 seconds
   3. 1 second
   4. 0.1 seconds

   Explanation: The time constant tau for an RC circuit is given by tau = R × C. Multiplying 2,000 ohms by 5 microfarads (0.000005 farads) results in 0.01 seconds. The other choices, such as 0.1 seconds, 1 second, and 10 seconds, result from incorrect multiplication or misplaced decimal points. Careful attention to units is required to avoid such common calculation errors.

2. RL Circuit Initial Response

   When a step voltage is suddenly applied to a series RL circuit, what is the initial current through the inductor immediately after the switch is closed?

   1. Double the maximum current
   2. Maximum possible amperes
   3. Half the maximum current
   4. Zero amperes

   Explanation: Immediately after the switch is closed, the inductor initially opposes any change in current, so the current is zero amperes. The maximum current can only be reached after the transient phase has passed. Current does not start at half or double the maximum; instead, it builds up gradually from zero due to the inductor’s opposition to sudden changes.

3. Passive Low-Pass RC Filter Function

   Which signal frequencies does a simple passive low-pass RC filter attenuate most strongly?

   1. DC signals only
   2. All frequencies equally
   3. Low frequencies
   4. High frequencies

   Explanation: A low-pass RC filter transmits low frequencies and attenuates, or reduces, high frequencies. DC signals (zero frequency) are not attenuated, and the filter does not affect all frequencies equally. Low frequencies are passed with minimal change, so options 'Low frequencies' and 'DC signals only' are incorrect.

4. Determining Circuit Order by Components

   If a circuit consists solely of one resistor and one inductor connected in series, what is the order of the resulting RL circuit?

   1. Second-order
   2. First-order
   3. Zero-order
   4. Third-order

   Explanation: An RL circuit with only a single resistor and a single inductor is classified as first-order because its response is described by a first-order differential equation. Second-order circuits require two energy storage elements, such as an LC or RLC configuration, and third-order involves even more complexity. There is no 'zero-order' designation in this context.

5. Voltage Across Capacitor During Charging

   During the charging of a capacitor through a resistor from a constant voltage source, how does the voltage across the capacitor change over time?

   1. It decreases exponentially toward zero
   2. It increases exponentially toward the supply voltage
   3. It oscillates with constant amplitude
   4. It remains constant

   Explanation: As a capacitor charges in an RC circuit, the voltage across it increases exponentially toward the supply voltage. It does not decrease toward zero, nor does it remain constant or oscillate, as would happen in circuits containing inductors and more complex arrangements. Only the exponential increase matches the observed charging behavior.