Node-voltage analysis

See attached file for full problem description. The circuit shown in Fig. P4.11 is a DC model of a residential power distribution circuit. a) Use the node-voltage method to find the branch currents i1 --i6. b) Test your solution for branch currents by showing that the total power dissipated equal to the total power developed.

Superposition principle

See attached file for full problem description.

Find Vout/Vin and cutoff frequency of the circuit

Please help me to find Vout/Vin and cutoff frequency of the circuit. Vout/Vin is also the transfer function of the circuit. The resistors values are 5k, 2.2k and 100 in case they are not clear. The capacitor is 15400uF. This is a lowpass filter. I need a step-by-step hand derived solution of Vout/Vin and cutoff frequency.

Derive an expression for the total impedance Zt.

Derive an expression for the total impedance Zt. See attached for full problem description.

KCL and Ohm's Law

(I have attached a picture of the problem.) With reference to Problem 2.7, use Kirchoff's current law and Ohm's law to find the resistances R1, R2, R3, R4, and R5 if R0=2 ohms. Assume R4=(2/3)R1 and R2=(1/3)R1. Problem 2.7 was about finding the currents using Kirchoff's current law knowing that i0=2A, i1=-4A, iS=8A and Vs=12V. The first step I took w/ this problem was to find the remaining currents. I found i3=2A and i2=6A. Next I set up Ohm's Law to solve for values of R: R=V/I I used the Vs, 12V for V. But I get R1=(12V)/(-4V)=-3V. R2=(12V)/(6V)=2V. R2 is supposed to be (1/3)R1 but 2 is not (1/3) of 3. Where am I going wrong?