Refer to the figure given below. The values of I1, I2 and I3 are . [figure]
- I1=2.5 A, I2=1.875 A, I3=1.875 A
- I1=1.875 A, I2=2.5 A, I3=1.875 A
- I1=1.875 A, I2=1.875 A, I3=2.5 A
- I1=2.5 A, I2=2.5 A, I3=1.875 A
Answer
(1) I1=2.5 A, I2=1.875 A, I3=1.875 A
Solution
Take the bottom node at 0 V ⇒ the top node is at 5 V (5 V cell, longer plate towards the top). Let the left node be at VL and the centre node at VM. In the middle branch the 10 V cell has its positive plate towards the left node.
[figure]
Middle branch (current I1 from M towards L): VL=VM+10-I1(1) ⇒ I1=VM+10-VL
Node M: 5-VM2= VM-02+I1 ⇒ I1=2.5-VM … (i)
Node L: I1= VL-54+ VL-04 ⇒ I1= 2VL-54 … (ii)
From (i): VL=VM+10-I1=2VM+7.5
Put in (ii): 2.5-VM= 4VM+104=VM+2.5 ⇒ VM=0, VL=7.5 V
∴ I1=2.5 A
I3= VL-04= 7.54=1.875 A
Current from L to the top node = 7.5-54=0.625 A; current from the top node to M = 5-02=2.5 A
Top node: I2+0.625=2.5 ⇒ I2=1.875 A
Answer: (1)