Answer to Question #117443 in Electric Circuits for Cecilia LeBrun

Question

I have a parallel circuit with resistors of 4 ohm and 2 ohm in a series that is parallel to a 3 ohm resistor with 4 amps next to it. No voltage listed. I need the total current, total voltage and the voltage of the 2 ohm resistor

Answer 1

Explanations & Calculations

• In a parallel combination same voltage is applied to each branch and the total current of the circuit is distributed over each branch at the common node, based on their individual branch resistance.
• The equivalent resistance of the top branch (with 2 resistors) = 4$\small \Omega$ +2$\small \Omega$ = 6$\small \Omega$.
• And applying V=i$\small \times$R, other information could be found.

1) Total voltage ; considering the 3$\small \Omega$ resistor,

$\qquad\qquad \begin{aligned} \small V &= \small 4A\times3\Omega \end{aligned}$

; considering the top branch,

$\qquad\qquad \begin{aligned} \small V &= \small i \times 6\Omega \end{aligned}$

Now,

$\qquad\qquad \begin{aligned} \small i \times 6\Omega & = \small 4 \times 3\\ \small i &= \small 2A \end{aligned}$

Therefore, total current is $\small i + 4A = \bold{6A}$

2) Total voltage is $\small V = 4A \times 3\Omega = \bold{12V}$

3) Voltage across 2$\small \Omega$ ,

$\qquad\qquad \begin{aligned} \small V_{2\Omega} &= \small iR\\ &= \small 2A \times2\Omega \\ &= \small \bold{4V} \end{aligned}$