Question

Problem 26.61

Find the current through each of the three resistors of the circuit shown in the figure (Figure 1). The emf sources have negligible internal resistance.

Part A

Find the current through 2.00-Ω resistor.

Part B

Find the current through 4.00-Ω resistor.

Part C

Find the current through 5.00 -Ω resistor.

Answer 1

See the diagram :

let i current flows through 5 ohm resistor.

and ii through 4 ohm resistor.

We will apply Kirchoff's junction law at B ,

current (i - i1) flows through 2 ohm resistor.

Now, applying Kirchoff's loop law in the loop ABEFA :

-20 - 4i1 +14 + 2(i - i1) = 0

=> 2i - 6i1 = 6

=> i - 3i1 = 3 ----- (i)

Now applying Kirchoff's loop law in the loop BCDEB :

5i - 36 + 4i1 = 0

=> 5i + 4i1 = 36 ------(ii)

Solving the equations (i) and (ii),

we get,

i = 120/19 A

i1 = 21/19 A

also, i - i1 = 99/19 A

Hence, current through 2 ohm resistor = 99/19 A.

current through 4 ohm resistor = 21/19 A.

current through 5 ohm resistor = 120/19 A.