**Part-1**

Q 1. For the circuit shown, determine

a) The time constant when the switch moves to position 1

b) The mathematical expression of v_{c}, i_{c} when the switch moves to position 1

c) v_{c} & i_{c} if the switch moves to position 2 at t=100ms

d) The mathematical expression of v_{c} & i_{c} when the switch moves to position 3 after it remained for 50ms on position 2.

e) Plot the waveforms of v_{c}, & i_{c} showing their behaviors in the time interval from t=0 to t=400ms.

Q2. For the given circuit, the switch is closed after the capacitors are fully charged.

a) What would be the initial value of v_{c}(t) when switch is closed?

b) Determine the time constants in both cases (switch is open, switch is closed).

c) Find v_{c}(t) & i_{c}(t) for t=1 m seconds, t=1.8m seconds and t=2.5m seconds

d) Plot the responses of v_{c}(t) & i_{c}(t) with time.

**Part-2**

Q 1. For the circuit shown, determine

a) The time constant z when the switch is closed

b) The inductor and resistor voltages and currents when the switch is closed.

c) The mathematical expression of *IL, vL *& *vR *when the switch is open at t=51.1. seconds.

d) v_{L} & i* _{L}* at t=3T

e) Plot the waveforms of *i _{L} *&

Q2. For the circuit shown, determine

a) The maximum values of *i _{L} *&

b) The inductor and resistor voltages and currents when the switch is closed.

c) The mathematical expression for inductor and resistors currents when the switch is open after inductor reaches its maximum* *current.

d) Resistor voltages at t=3T

e) Plot the waveforms of i_{L} & v_{L}.

Q3. For the given circuit, the capacitor and inductors have reached the steady state. Determine V_{L}, I_{L} & *I _{2}.*

* *

**Part-3**

Q1. Write down the following expressions in terms of sine function:

*a. cosα = sin(?)*

* *

*b. -sinα = sin(?)*

* *

*c. -cosα = sin(?)*

* *

Q2. For the given periodic waveform, Determine

a) T b) f c) V_{max} and v_{p-p} d) number of cycles shown* *

Q.3 If v(t) = 300sin(157t), how long in seconds does it take this waveform to complete 1/2 cycle.

Q4. Write the analytical expression for the given waveforms

Q5 If a periodic waveform has a frequency of 20Hz, how long in seconds will it takes to complete 5 cycles?* *

*Q6 Find the phase relation between the following signals:*

* ** *

*a. v = -5 sin(ωt + 75°) & i = 10 cos(**ωt* -130°)

* *

*b. v = -3 cos(**ωt*) & i = 8sin(* ωt* + 55° )

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