Question

The circuit in the figure on the right shows a network of resistors

connected in series and in parallel.

(a) Determine the total resistance of the network.

(b) What is the current through the 3.00-Ω?

Answer 1

Series combination

$R_t=R_1+R_2+R_3$

$R_t=3+3+3=9\Omega$

Parallel combination

$\frac{1}{R_t}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

$\frac{1}{R_t}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}$

$R_t=\frac{R}{3}\Omega$

(B)

R=3$\Omega$ Resistance current flow

Current

Assume (V)=3V

Series combination current

$I=\frac{V}{R_t}$

$I=\frac{3}{9}=0.33A$

Parallel combination

Voltage drop all resistance equal

$I=\frac{3}{3}=1A$