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CBSE Class 12 Physics 2013 Paper

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Question : 16 of 29
Marks: +1, -0
Use Kirchhoff's rules to determine the value of the current I1I_1 flowing in the circuit shown in the figure.
Solution:  
The given circuit:
At node MM, applying KCL\mathrm{KCL},
I3=I1+I2I_3=I_1+I_2
In loop MPQN, applying KVL,
  20I3+30I1  =20\;20 I_3+30 I_1\;=20
   Or,     20(I1+I2)+30I1  =20\; \text{ Or, }\; \;20 (I_1+I_2) +30 I_1\;=20
   Or,     50I1+20I2  =20\; \text{ Or, }\; \;50 I_1+20 I_2\;=20
   Or,     5I1+2I2  =2\; \text{ Or, }\; \;5 I_1+2 I_2\;=2 .......(i)
In loop MSTN, applying KVL,
  −20I2−20I3  =−20−80=−100\;-20 I_2-20 I_3\;=-20-80=-100
   Or,     −20I2−20(I1+I2)  =−100\; \text{ Or, }\; \;-20 I_2-20 (I_1+I_2) \;=-100
   Or,     −20I1−40I2  =−100\; \text{ Or, }\; \;-20 I_1-40 I_2\;=-100
   Or,     −I1−2I2  =−5\; \text{ Or, }\; \;-I_1-2 I_2\;=-5 .......(ii)
Solving equations (i) and (ii)
I1=−  34AI_1=-\; \frac{3}{4} \mathrm{A}
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