question_answer

The magnitude of i in ampere unit is                      [KCET 2005]

A)                    0.1

B)                    0.3

C)                    0.6

D)                    None of these

Correct Answer: A

Solution :

           Applying Kirchoff's law in following figure. At junction A : \[i+{{i}_{1}}+{{i}_{2}}=1\] .... (i) For Loop (i) \[-\,60\,i+(15+5){{i}_{1}}=0\]      Þ \[{{i}_{1}}=3i\]         ...(ii) For loop (2) ? (15 + 5) i1 + 10 i2 = 0 Þ i2 = i1 = (3 i) = 6i On solving equation (i), (ii) and (iii) we get i = 0.1 A Short Trick : Branch current =      \[\,\text{main current }\left( \frac{\text{Resistance of opposite branch}}{\text{Total resistance}} \right)\] Þ\[i=1\times \left[ \frac{\frac{20}{3}}{\frac{20}{3}+60} \right]\]       = 0.1 A