Question

the equivalent resistance between a and f in the circuit shown in the figure is

Answer 1

Answer:

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Answer 2

The equivalent resistance between a and f in the circuit is 5/6 Ω

Given:

circuit diagram with resistors connected in series and parallel

to find:

equivalent resistance between A and F

solution:

We can calculate the equivalent resistance between a and f by the following method:

firstly we have to re-draw the circuit diagram in order to identify the series and parallel connected resistors.

In series connections, the total resistance is calculated by taking the sum of the resistance connected in series.

                               $R_{T} = R_{1} +R_{2} + ....... + R_{n}$

In parallel connections, the total resistance is calculated by

                                $\frac{1}{R_{T}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + ....+ \frac{1}{R_{n}}$

please refer to the attached diagram for abetter understanding.

please note that B,D,F   points are directly connected.

so we can consider them as a single point with no potential difference.

now, resistance between C and F in series is: 4Ω +2Ω = 6Ω

now we have two resistors connected in parallel from C to D, F

so the equivalent resistance between C to D, F is=

$\frac{1}{R_{T}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

$\frac{1}{R_{T}} = \frac{1}{6} + \frac{1}{6}$

$\frac{1}{R_{T}} = \frac{2}{6}$

$R_{T} = 3$ Ω

now, the resistance between A to C to D in series is: 2Ω +3Ω = 5Ω

now we have two resistors connected parallel from A to B,D,F

so the equivalent resistance between A to B, D, F is=

$\frac{1}{R_{T}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

$\frac{1}{R_{T}} = \frac{6}{5\\}$

$R_{eq} = \frac{5}{6}$ Ω  

Hence, The equivalent resistance between a and f in the circuit is

5/6 Ω.

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