**72. The circuit shown in the drawing is constructed with six identical resistors and an ideal battery. When the resistor R4 is removed from the circuit, the current in the battery decreases by 1.9 A. Determine the resistance of each resistor.

First we need the total resistance. So starting away from power source we have R₁, R₃, and R₅ all in series so we can add them and R_eff1 = 3R and our circuit looks like

Now add the 3R and R in parallel and we get

And the circuit now looks like

Now we have three resistors in series so the total resistance is

So the current is

Now if only R₄ is removed the circuit looks like this

In this case we have 5 resistors all value R in series, so

And current now is

Finally problem tells us that

Now solve for R

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This page last updated on June 18, 2018