Find equivalent resistance

Asked by ojastej235 | 29th Sep, 2021, 07:56: PM

Expert Answer:

 
It is assumed equivalent resistance across battery is to be determined.
 
If we see the given circuit , we have 50 Ω resistors are connected at  both side of 200 Ω resistor ( near point marked as e in given circuit ) .
 
Hence the series combination of 50 Ω, 200 Ω and 50 Ω is replaced by a 300  Ω resistance .
 
500 Ω resistance connected between b and c is redrawn as shown in above figure .
 
Let us assume current distribution as shown in figure.
 
If we apply Kirchoff's voltage law to the closed loop ABDEF , we get
 
50 i1 + 500 i3 + 100 i6 + 50 i1  = 10  .........................(1)
 
At node D ,  i6 = i3 + i4  ..........................(2)
 
Using eqn.(2) , we rewrite eqn.(1) as  ,  100 i1 + 600 i3 + 100 i4  = 10   ............................ (3)
 
If we apply Kirchoff's voltage law to the closed loop BCDB , we get
 
100 i2 + 300 i4 - 500 i3 = 0 ..................................(4)
 
At node B , we have , i1 = i2 + i3   ...........................(5)
 
Using eqn.(5) , we rewrite eqn.(3) as ,  100 i2 + 700 i3 + 100 i4 = 10  ........................... (6)
 
By subtracting eqn.(4) from eqn.(6) , we get ,  1200 i3 - 200 i4 = 10  .............................(7)

If we apply Kirchoff's voltage law to the closed loop CEDC , we get
 
500 i5 - 100 i6 - 300 i4 = 0   .......................... (8)
 
at Node C , i5 = i2 - i4 .......................(9)

By using eqn.(2) and eqn.(9) , we rewrite eqn.(8) as
 
500 i2 - 100 i3 - 900 i4 = 0 ......................(10)
 
By multiplying eqn.(4) by 5 and subtracting from eqn.(8) ,
 
we get , i3 = i4 ...................(11)
 
Using eqn.(11) , we get i3 from eqn.(7) as  i3 = ( 1/100 ) A
 
Hence we have , i3 = i4 = ( 1/100 ) A
 
Using values of i3 and i4 in eqn.(10) , we get i2 = 2/100 A
 
Hence , i1 = i2 + i3 = (1/100) +(2/100)  A  = (3/100) A
 
Since current drawn from battery is  i1 = (3/100) A , 
 
Equivalent resistance = Voltage /current = 10 / (3/100)  = 333.33 Ω
 

Answered by Thiyagarajan K | 29th Sep, 2021, 11:33: PM