# How to solve circuit problems with resistors in parallel then in series?

A problem I am doing shows a circuit with one battery and one resistor. Then a switch is closed and two additional resistors are added in paralell and another in series as shown in the picture. (all $R = 2 \Omega$, $\Delta V=12$ V).

The book says that the current through the original resistor will NOT change despite change in the total resistance.

After diagraming it out i see that but i struggle to find the current in the other parts of the circuit

I would find total equivaent resistance. Then using the voltage of the battery find the current of the original resistor.

Then for the other branch on the right, how do i handle the voltage drop becsuse i also have the resistor in series next downstream? Additionally current starts from the big line/top and goes right! so up and right in my textbook.

## 2 Answers

Hints:

If you figure out the equivalent resistance of $R_V$, $R_{VI}$ and $R_{VII}$, you can figure out the current through $R_{VII}$.

If you know the current through $R_{VII}$, you can figure out the voltage across $R_{VII}$.

If you know the voltage across $R_{VII}$, you can figure out the voltage across $R_V$ and $R_{VI}$.

If you know the voltage across $R_V$ and $R_{VI}$, calculating the current through each of those is easy.

• my textbook has current starting from the larger line (bigger line for positive smaller for negative). would the same directions apply? – Kevin Lee Feb 26 '18 at 20:29

In problems like this (a closed, DC voltage, resistor network), the voltage supply is assumed to be able to supply any current necessary to meet the steady-state behavior. So, the following principles apply:

• 1a) Circuit elements in parallel have the same voltage. So the $R_{V},R_{VI},R_{VII}$ combination has the same voltage as the supply.
• 1b) Circuit elements in parallel may have different currents but the currents will add at the common connection point. So the currents through $R_{V}$ and $R_{VI}$ will add together.
• 2a) Circuit elements in series have the same current. So the $R_{V},R_{VI}$ combination (parallel) has the same current as the $R_{VII}$ resistor.
• 2b) Circuit elements in series may have different voltages, but each voltage drop will add to the previous drop.

There is no need to find the total resistance for this circuit, unless you are asked for it.