For the circuit shown to the right, determine the magnitude of the currents 2, l

Question

For the circuit shown to the right, determine the magnitude of the currents 2, l3, and l4 assing through batteries 2, 3, and 4, respectively. In each case, determine whether the attery is supplying power or being charged. The batteries and resistors in the circuit are assumed to be ideal and have the following properties: ,-27.0 V -450 V E,-22.5 v E,-4.50 v Ri-39.0 R,-30.0 R3-61.0 Number O supplying power being charged A R2 O supplying powe being charged Number A Number O supplying power 14 = A O being charged

Explanation / Answer

Applying Kirchoff's Voltage rule in left loop :

E3 = i3*R3 + E4

So, 22.5 = i3*61 + 4.5

So, i3 = 0.295 A

Now, for the right loop :

E4 = i2*R2 - E2 + E1 + i2*R1

So, 4.5 = i2*30 - 4.5 + 27 + i2*39

So, i2 = -0.261 A

So, I2 = 0.261 A <------ being charged (due to the negative sign)

I3 = 0.295 A <---------- supplying power

I4 = I2 + I3 = 0.261 + 0.295 = 0.556 A <--------- being charged

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