Question

# What is the current flowing through the 10 Ω resistor in the figure below?

A
0.1 A
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B
0.2 A
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C
0.3 A
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D
0.4 A
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Solution

## The correct option is B 0.2 AAs the current flows from a higher potential to a lower potential, the current direction is as shown below from node 1 to node 0. If voltage at node 0 is V0 then applying Kirchoff's loop law, the current i through the 10 Ω is given by: i=10−V010 ⟹ 10−V0=10i -- (1) Consider the currents flowing through 20 Ω and 30 Ω be i2 and i3 respectively. Again applying kirchhoff's loop law for node 2 and 3 respectively. V0−720=i2 or, V0−7=20 i2 ------ (2) V0−530=i3 or, V0−5=30 i3 ------ (3) Adding equations (1) & (2) we will get 3=10 i+20 i2 3 =30 i2+10 i3 (as i=i2+i3) 30i2+10i3=3 --------- (4) Now adding equation (1) and (3), we will get 5=10 i+30 i3 5 =10 i2+40 i3 (as i=i2+i3) 10i2+40i3=5 --------- (5) Solving equation (4) and (5), we get i2=7110 i3=12110 and, i=i2+i3=19110 A≈0.2 A

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