Question 1 of 5 Map A pling leaming For the circuit shown to the right, determin

Question

Question 1 of 5 Map A pling leaming For the circuit shown to the right, determine the magnitude of the currents l2, 13, and passing through batteries 2, 3, and 4, respectively. In each case, determine whether the battery is supplying power or being charged. The batteries and resistors in the circuit are assumed to be ideal and have the following properties E. 30.0 V E. 4.50 V E3-25.5 V E, 3.00 V RI 23.0 Q 24.0 Q R1 73.0 Q Number O supplying power A o being charged Number O supplying power A O being charged Number O supplying power A O being charged A Previous Check Answer Next Ext O Hint

Explanation / Answer

E1 = 30 V

E2 = 4.5 V

E3 = 25.5 V

E4 = 3 V

R1 = 23 ohms

R2 = 24 ohms

R3 = 73 ohms

Assuming current in the first loop is clockwise and is i1

and current in the 2nd loop is clockwise and is i2

Applying Kirchoffs Laws in the 2 loops

1st loop

- E3 + E4 - i1 R3 = 0

- 25.5 + 3 - i1 *73 = 0

i1 = (3 - 25.5)/73 = - 0.3082 A

2nd loop

- E4 - i2*R1 + E1 - E2 - i2*R2 = 0

- 3 - i2*23 + 30 - 4.5 - i2*24 = 0

i2 = (30 - 3- 4.5)/(24 + 23) = 0.4787 A

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I2 = i2 = 0.478 A , battery is being charged

I3 = i1 = 0.3082 A , supplying power

I4   = i1 - i2 = | - 0.3082 - 0.478 | = 0.7862 A , battery is being charged

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