P 3.6-11 Find i and R_{eq a–b} if v_ab = 40 V in the circuit of Figure P 3.6-11.

Answer: R_{eq a–b} = 8 Ω, i = 5/6 A

Figure P 3.6-11

We have two sets of resistors in series that are in parallel. On the right we have a 6 Ω and a 2 Ω in series which is 8 Ω, and we have a 3Ω and 5 Ω in series which also makes 8 Ω so we can redraw the circuit as

So we now have two 8 Ω resistors in parallel which makes an effective resistor of 4 Ω so that in series with a 20 Ω gives us a 24 Ω in parallel with a 12 Ω gives a total resistance of

So

Now if we add a voltage source we get the following circuit

We can find i_tot from

Recall that R_eff in parallel with the 12 Ω resistor is 24 Ω, so 1/3 of current goes into the 20 Ω resistor. SO

Finally i is then result of splitting by two equal resistors so it is one-half of i₂

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This page last updated on January 20, 2019