Question

Consider the group of resistors shown in the figure below, where R1 = 4.5 Ω and script e = 8.1 V.



(a) Find the current in each resistor in the figure.
I4.5=
I9.8=
I1.2=
I6.7=


(b) Is the potential at point A greater than, less than, or equal to the potential at point B?


Explain.


(c) Determine the potential difference between the points A and B.

Answer 1

From the circuit diagram i = i₁ + i₂    

In the first loop, apply Kirchoff's voltage law

0 = 12 V - i(4.5 Ω) - i₁(1.2 Ω) - i(9.8 Ω)

1.2i₁ = 12 - 14.3i

i₁ = 10 - 11.91i

In the whole loop, apply Kirchoff's voltage law

0 = 12 V - i(4.5 Ω) - i₂(6.7 Ω) - 8.1 V - i(9.8 Ω)

6.7i₂ = 3.9 - 14.3i

i₂ = 0.58 - 2.13i

Therefore

i = 10 - 11.91i + 0.58 - 2.13i

15.03 i = 10.58

i = 0.704 A

Therefore

i₁ = 1.61 A

i₂ = -0.919 A

Therefore the current through the components

I_4.5 = 0.704 A
I_9.8 = 0.704 A
I_1.2 = 1.61 A
I_6.7 = 0.919 A

b)

The potential at A is greater than that at B because the resistaor 1.2 Ω between the points A and B decreases the potential at B

c)

The potential difference between A and B is given by

V_A - V_B = i₁(1.2 Ω)

              = (1.61 A)(1.2 Ω)

              = 1.932 A