Find the voltage, Vc(t), over the capacitor for all time t>0.

The
voltage source Vs in the circuit shown below is nominally 5V. A power surge
at time t=0 causes it to instantaneously jump to 10V, and then at time t=5ms,
it instantaneously drops back to 5V. Express the current flowing down through
the 30 ohm resistor (as a function of time).

a) What is the 30 ohm resistor current at t=0+?

b) What would the final 30 ohm resistor current be if Vs stayed at 10V?

c) What is the 30 ohm resistor current at t=5ms+?

d) What is the final 30 ohm resistor current?

e ) Write the full expression(s) for the 30 ohm resistor current as a function
of time.

The switch in the circuit shown below closes at t=0 and then opens at time t=5ms. Solve for the voltage Vx over the 3K resistor (as a function of time).

Design a circuit that has a critically damped response using a 10mH inductor, a 1mF capacitor, a 10 V source with a 5 O internal source resistance, and a load resistance that you choose.

In the circuit shown above, the switch is controlled by the voltage Vx:

Vx > 2V, the switch opens

Vx < 0.1V, the switch closes

A sketch of the voltage Vx over time is shown below (the scale of each axis is not shown). Give a mathematical expression to describe Vx during the first period. You will need to describe it in two different portions of time: as Vx rises and as Vx falls, so be sure to note the time range during which your formula is valid.

You and your lab partner wire the circuit shon below on a protoboard. However, the 2 KW resistor is inserted in the board poorly and when your partner touches the resistor it becomes disconnected momentarily from the circuit at time 0 and then reconnected after 100ms.

(a) Describe the current i(t) flowing right through the 8KΩ resistor by providing the mathematical formula(s) for t>0 (split into multiple intervals if needed, but clearly label the time range of each interval).

(b) Sketch a graph of i(t) for t>0.

A 12-V power supply is connected to a 1K ohm resistor and a 3mF capacitor which are in series. The power supply has an internal source resistance of approximately 50 ohms.

(a) Draw a diagram to model this circuit

(b) How long will it take the circuit to reach steady-state from the time the power supply is switched on?

(c) Sketch the current through the 1K ohm resistor as a function of time.

Given a course voltage of 10V, a source resistance of 10 ohms, a 10mH inductor, and a 5nF capacitor, choose a load resistance and draw a circuit that will have an underdamped (decaying sine wave) second order transient response.

You and your lab partner wire the circuit shown below on a protoboard. However, the voltage source is poorly connected to the board and when your partner jiggles the cable, it becomes disconnected momentarily from the circuit at time 0 and then reconnected after 100ms.

a) Use transient analysis to describe the current i(t) flowing right through the 8 Kohm resistor by providing the mathematical formula(s) for t>0 (split into multiple intervals if needed, but clearly label the time range of each interval).

b) Sketch a graph of i(t) for t>0.

c) What is the current at time 50ms and at time 150ms?

- What went wrong? Quantify.
- What resistor value should you have used?
- How long will it take the capacitor to charge up using the new resistor?

- Label the graph scales to show the quantified maximum and quantified minimum current that flows.
- At what time is the current in R2 slightly more than half way between the maximum and minimum?
- At what time is the current in R2 at exactly 20.0 mA?

(c) 2014, Steven H. VanderLeest