E84 Homework 4

1. In the voltage divider circuit below, $V_0=20V$, $R_1=R_2=500\Omega$. Use Thevenin's theorem to find the current through and voltage across the load resistor $R_L$ when it is $100\Omega$, $200\Omega$, $300\Omega$, respectively.

   

2. Using Thevenin's theorem to determine the current in the $3-\Omega$ resistor of the following figure.

   

3. Find voltage across and the current through the 10-$\Omega$ resistor.

   

4. Find all currents in the diagram in which V=120V, $R_1=2\Omega$, $R_2=20\Omega$. Hint: it is very hard to solve the problem by finding the currents in the order of $I_1$, $I_3$, $I_5$, as computing the resistances of the resistor network is tedious. However, it is much more straight forward to find the currents in the order of $I_5$, $I_3$, $I_1$, if you assume $I_5$ is known, e.g., $I_5=1A$. However, the voltage for the voltage source obtained based on this assumption is of course not as given (120V). In this case, the linearity property $F(ax+by)=aF(x)+bF(y)$ can be applied. In particular, given $y=F(x)$, then $ay=F(ax)=aF(x)$. Use this relationship to find the actual values of the currents.

   

5. In the circuit below, $R_1=1\Omega$, $V_2=2V$, $R_3=1\Omega$, $R_4=3\Omega$ $I_5=5A$, $V_6=2V$, and $R_6=1\Omega$. Find
   1. current through voltage source $V_2$.
   2. current through resistor $R_3$
   (Hint: consider superposition theorem.)

   

6. In the circuit below, $R_1=1\Omega$, $R_2=2\Omega$, $R_3=3\Omega$, $R_4=4\Omega$, $R_5=5\Omega$, $V_1=4V$, $V_2=5V$. Find voltage $V$ across and current $I$ through the load resistor $R_3$ by converting the rest of the circuit into a
   • Thevenin's voltage source $V_T$ with $R_T$
   • Norton's current source $I_N$ with $R_N$
   Verify your results by converting the current source into a voltage source (or vise versa). Then find voltage $V$ and current $I$ associated with load $R_3$.