# Circuits – Calculating Effectice Resistance

1. The problem statement, all variables and given/known data

Calculate the effective resistance for the circuits below.

A.

B:

Sorry for my crude drawings but I thought it was easiest and quickest this way.
2. Relevant equations
$$R_{series}=\sum\limits_{i=1}^n R_i \\ \frac{1}{R_{parallel}}=\sum\limits_{i=1}^n \frac{1}{R_i}$$

3. The attempt at a solution

We have never been told how to calculate the effective resistance where both series and parallel occur, only how to do it if it is series and how to do it if it is parallel. But using intuition for part A i just did the bit in series and then the bit in parallel and added them like below.

$$\sum\limits_{i=1}^n R_i = 2+2=4 \\ \sum\limits_{i=1}^n \frac{1}{R_i} = \frac{1}{2}+\frac{1}{2} = 1 ∴ R=1 \\ ∴R_{total}=4+1=5Ω$$

For part B I am scratching my head as to where to start because the whole thing is in parallel and then there are parrellel bits inside of that iyswim. Any hints on how to approach part B would be much appreciated, thanks.

http://ift.tt/1esNJrv