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In the circuit if Vi=120V then calculate the voltage V0 across the impedance j60. Provide the steps.
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Asked by miaowmira1900 | 31 Jul, 2019, 00:34: AM
answered-by-expert Expert Answer
 
Let i is the net current drawn from potential difference Vi across A and B. 
 
Let i1 , i2 and i3 be the current passing through  impedences 10Ω , 30Ω and 60Ω respectively.
 
Hence current passing through 40Ω resistance is (i-i1)
 
we have four unknowns i.e., i, i1 , i2 and i3 , hence we need four equations to solve.
 
we have the following equations.
 
At node-C,  i = i1 + i2 + i3    ....................... (1)
 
Applying kirchoff's rule for the path A-B-C-D,    20 i + 10 i1 = Vi .............(2)
using eqn.(1), eqn.(2) is rewritten as ,  30 i1 + 20 i2 + 20 i3 = Vi ........................(3)
 
Applying kirchoff's rule for the path B-E-F-C-B,    -40 (i-i1) - 30 i2 + 10 i1 = 0 .............(4)
using eqn.(1), eqn.(4) is rewritten as ,  10 i1 - 70 i2 - 40 i3 = 0  ........................(5)
 
Applying kirchoff's rule for the path E-G-H-F-E,  - 30 i3 -60 i3 + 30 i2 = 0    or      i2 = 3 i3  .............(6)
 
By solving eqn.(3), eqn.(5) and eqn.(6),  we get i1 = (25/830) Vi  ,  i2 = (3/830) Vi  and  i3 = (1/830) Vi
 
voltage across impedence 60Ω ,  i3 × 60  = (6/83) Vi
 
Answered by Thiyagarajan K | 31 Jul, 2019, 15:25: PM

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