Adjusting Resistance to achieve maximum power dissipation

Adjusting Resistance to achieve maximum power dissipation. See attached file for full problem description. Please answer number 7.4 only.

Determine Load Impedance and Time-Average Power Delivery

Determine Load Impedance and Time-Average Power Delivery. See attached file for full problem description. Please answer number 7.5 only.

Calculate Step Response

Problem 1 only. See attached file for full problem description. In the following circuit, v1(t) is the input voltage and v2(t) is the output voltage. Calculate the step response of the system. i.e., calculate the output v2(t) when the input is a unit step function.

Calculate the Step Response

Number 2 Only. See attached file for full problem description. In the following circuit, all of the resistors R are identical, i1(t) is the input current and i2(t) is the output current. Calculate the step response of the system. i.e., calculate the output i2(t) when the input is a unit step function. Please express your answer as a function of time, in terms of the parameters L and R.

RLC circuit

See attached file for full problem description. (a) suppose the voltage v(t) in the above circuit is given by: V(t) = (0.006)t*exp(-4000t) Determine the values of the resistor R and capacitor C (b) Repeat (a) for the case where v(t) = 4exp(-2000t) – 3exp(-800t) (c) Repeat (a) for the case where v(t) =2*sin(4000t)*exp(-3000t) (d) For the case considered in (c), calculate the voltage across the inductor VL(t).