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Laws and Circuit Analysis

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- Find the equivalent resitstance between terminals A and B.
- Between C and D.
- Between B and C.

- Find the Thevenin equivalent between nodes B and C. Do it once without using superposition, and once with it.
- Find the Thevenin equivalent between nodes A and C. Use any method

- Find the Thevenin equivalent between nodes A and B.
- Between C and D.

- Find Rx such that the power dissipated through it is maximized (hint: find the Thevenin equivalent circuit experienced by Rx and use maximum power transfer)
- With the value of Rx chosen, find the power dissipated in Rx, and the total power dissipated in the other resistors.

- the input has been zero volts for a long time, and then goes to 1 volt.
- the input has been 1 volt for a long time, and then goes to -1 volt.

The resistor has value=R, and the capacitor has value=C.

For the two circuits of the previous problem, with R=1kΩ, C=1uF:

- Construct the Bode plots.
- From the Bode plots determine the output voltage if the input is 10sin(100t).
- Determine the output voltage if the input is 10sin(10000t).
- What type of filtering operation does each circuit perform?

For the circuit shown find v_{x}(t) if:

- the switch has been closed for a long time, and is opened at t=0.
- the switch has been open a long time and is closed at t=0.

R1=R2=R3=1kΩ, C=1uF.

Solve for the two cases given.

- The voltage across the capacitor is 1/3 V1 at t=0 when the switch opens. Solve for the time at which the voltage across the capacitor is 2/3 V1.
- The voltage across the capacitor is 2/3 V1 at t=0 when the switch closes. Solve for the time at which the voltage across the capacitor is 1/3 V1 if at t=0:

For the circuit shown

- The capacitor is charged to 2.2 V when the switch is closed at t=0,. Calculate how long it takes the voltage across the capacitor to go from 2.2V (at t=0) to 1.4V.
- The capacitor is charged to1.4 V when the switch is opened at t=0. Calculate how long it takes the voltage across the capacitor to go from 1.4V (at t=0) to 2.2V. Since R5 is so much less than the other resistances in the circuit, assume it has a value of 0 for this part of the problem.
- (extra - you need not do this) Repeat the previous part without assuming R5=0Ω.

If the voltage (or any other quantity) in a
first order system starts at v(0^{+}) and ends at v(∞), show that
the time time, t_{1}, at which it reaches the voltage v_{1} (i.e.,
v(t_{1})=v_{1}) is given by:

- What type of filter is this? Make your argument without equations, based upon the low and high frequency behavior of the circuit elements.
- Find the transfer function (V
_{o}(s)/V_{i}(s)) - Verify that your transfer function agrees with part a.
- Does the damping factor increase or decrease as R increases?

For the circuit shown:

- What type of filter is this? Make your argument without equations, based upon the low and high frequency behavior of the circuit elements.
- Find the transfer function (V
_{o}(s)/V_{i}(s)) - Verify that your transfer function agrees with part a.
- Does the damping factor increase or decrease as R increases?

The circuit shown is a Wheatstone bridge, and is often use to measure small changes in resistance (denoted by the lowercase "r").

- Show that when r=0, V
_{o}=0. - Derive an expression for V
_{o}in terms of V_{i}, R, and r. - If r<<R, find a linear approximation for Vo in terms
of V
_{i}, R and r.

For the circuit shown:

- Find the voltage between B and C using superposition.
- Find the voltage between A and C.

The resistor network shown repeats forever to the
right. What is the equivalent seen between A and B?
All resistors are equal with resistance R.

Hint: The resistance to the right of A/B is
the same as the resistance to the right of C/D.