E84 Homework 3

1. While various voltage sources such as batteries are very common in everyday life, current sources are not widely available. One type of current source is the photocells, which generates current proportional to the intensity of the incoming light. Also, certain specially designed transistor circuits can generate to output constant current. Moreover, as discussed in class, any current source can be obtained by converting a corresponding voltage source. Design a current source with $I_0=10$ mA and $R_0=1\;K\Omega$ by converting a voltage source. Find its voltate $V_0$ and internal resistance $R_0$.

2. The circuit below (assuming $I_0=1A$, $R=3\Omega$, $V_0=2V$) was discussed in class in terms of power delivery, absoption or dissipation of each element in the circuit. Now redo the problem assuming the polarity of the voltage source is reversed (negative on top).

   

3. The output resistance of the power amplification circuit of a Hi-Fi system is $R_{out}=8\Omega$ and the output voltage is $V_{out}=20V$. Find the power received by the speaker, the total power consumption, and the power efficiency of the circuit, for each of the three speakers with resistance: $R_L=4\Ogema$, $R_L=8\Ogema$, and $R_L=16\Ogema$

4. Find the optimal load resistance $R_L$ so that it receives maximal power from the current source $I_0=10A$ with internal resistance $R_0=1\Omega$ and power transmission line resistance $R_T=9\Omega$. Find the maximum load power and the power loss along the transmission line.

   

   To verify your choice of load resistance, show that the power consumption of the load will always be lower than this maximum when its resistance is either increased or decreased by ten percent.

5. Convert the following circuit into (a) an equivalent current source $(I_{cs}, R_{cs})$ and then (b) an equivalent voltage source $(V_{vs}, R_{vs})$. Give an expression for the load $R_L$ so that it will receive maximum power from the source.

   

6. Solve the homework problem (Example 4) on this page, but treating the middle node as the ground.

7. Find all node voltages in the circuit with respect to the bottom node as ground, where $R_1=100\Omega$, $R_2=5\Omega$, $R_3=200\Omega$, $R_4=50\Omega$, $V=50V$, $I=0.2A$. Use both node voltage and loop current methods to solve this circuit. Choose independent loops and nodes wisely to simplify your computation.