12. Five resistors are connected as shown in the diagram. The potential differen

Question

12. Five resistors are connected as shown in the diagram. The potential difference between points A & B is 25 V

12a.- What is the equivalent resistance between the points A and B?

a)1.5 b) 4.8 c) 7.5 d) 9.4

12b.- What is the current through the 1.8 resistor?

a) 2.8 A, b) 3.3 A c) 5.6 A d) 6.9 A

12. Five resistors are connected as shown in the diagram. The potential difference between points A & B is 25 V 12a.What is the equivalent resistance between the points A and B? a)1.5 omega b) 4.8 omega c) 7.5 omega d) 9.4 omega 12b.- What is the current through the 1.8 omega resistor? a) 2.8 A, b) 3.3 A c) 5.6 A d) 6.9 A

Explanation / Answer

12a. 3.5 and 5.1 resistors in series = 3.5+5.1 = 8.6. 8.6 in parallel with 1.8 = 1/(1/8.6 + 1/1.8) = 1.5. 1.5 in series with 3.6 and 2.4 is total equivalent resistance of 1.5 + 3.6 + 2.4 = 7.5, choice c.

12b. Total current through equivalent resistance of 7.5 is given by I = V/R = 25V/7.5 = 3.33A. Now to split the resistances back apart, there are 3.33A flowing throught the equivalent resistance of 1.5 found in part a (1.8 in parallel with 8.6). To find the current flowing just through the 1.8, remember that voltage is the same in parallel. So since V = IR, I1*1.8 = I2*8.6, and I1+I2 = 3.33A --> I2 = 3.33A - I1. Substitute that in so you end up with two equations in terms of I1 (the current through the 1.8 resistor):

1.8I1 = (3.33-I1)*8.6 = 28.638 - 8.6I1
10.4I1 = 28.638
I1 = 2.75A 2.8A, choice a.

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