Second Order Circuit

Find i(t)?

Equivalent resistance problem 4

Problem 4:

Find $R_{ab}$?

Answer: $5\Omega$  

Equivalent resistance problem 3

Problem 3:

Find $R_{ab}$?

Answer: $R$

Equivalent resistance problem 2

Problem 2:

Find $R_{ab}$?

Answer: $\frac{R}{3}$

Equivalent resistance problem 1

Problem 1:

Find $R_{ab}$?

Answer: $4\Omega $ 

Star-Delta transformation

Find $R_a$?

Solution:

                $R_a=R_1+R_2+\frac{R_1R_2}{R_3}$

• If $R_1=R_2=R_3=R_Y$ then find $R_{\Delta }$?

      Solution: $R_{\Delta }=3R_Y$

Series and Parallel circuits practice exercise

Problem 1:

Find $R_{ab}$=?

        $R_{cd}$=?

        $R_{ac}$=?

Solution: $R_{ab}=\left(R_1+R_3\right)=R_{ad}$

               $R_{cd}=\left(R_1+R_3\right)=R_{cb}$

               $R_{ac}=\left(R_1+R_2\right)$

Series and Parallel

Problem 1:

Find $R_{ab}$?

Solution: $R_{ab}=R_1+R_2$

Capacitors in Parallel

$C_T=C_1C_2$

Capacitors in Series

Find Equivalent Capacitance between a and b ($C_T$)?  

Solution: $C_T=\frac{C_1C_2}{C_1+C_2}$

Energy stored in Capacitor

$E=\frac{1}{2}Cv^2$

Energy stored in Inductor

$E=\frac{1}{2}Li^2$

Current through Inductor

$i=\frac{1}{L}\int Vdt$

Voltage across Capacitor

$V_c=\frac{1}{C}\int _0^ti\left(t\right)dt$

Parallel Circuit

Find $I_1$, $I_2$, $I_3$, $I$?

Solution: $I_1=\frac{V}{R_1}$

$I_2=\frac{V}{R_2}$

$I_3=\frac{V}{R_3}$

$I=I_1+I_2+I_3$

$I=\frac{V}{R_1}+\frac{V}{R2}+\frac{V}{R_3}$

$I=\frac{V}{R_1+R_2+R_3}$

Series Circuit

Find I?

Solution: $I=\frac{V}{R_1+R_2+R_3}$

Basic circuit

Find I?

Solution: $I=\frac{V}{R}$