Point A is between D and G To calculate the potential difference between any two

Question

Point A is between D and G

To calculate the potential difference between any two points in a network you need first to know the true directions of the currents in the different branches of the network and then apply the formula: Traversing any branch from point B to point A and restricting yourself to the sign convention explained in the theory. Draw the network shown in Figure 2 indicating the magnitudes of Ei and E2 as measured. Indicates also the magnitudes and the true sense of direction of the currents Ii, I2 and I3. Calculate following three different paths: BA; BCDA and BFGA and make sure that you get the same answer in the three paths. Answers

Explanation / Answer

Across AB

V(ab) =Va-Vb = - 5 I2 + E2 .........................eq 1

Across BCDA(when switch K1 closed )

V(ab) =Va-Vb = E1 +10 I1 ................................eq2

when switch K1 open

Vab = 0

Across BFGA(when switch K1 closed )

V(ab) =Va-Vb = -20 I3 ...........................................eq=3

when switch K2 open

Vab = 0

also applying kirchoffs rule we get
I1= I2+I3 ...................................................................eq4
E1 = 3.9 V and E2 = 6.35 V
solving all the equation we get
- 5 I2 + E2 = E1 +10 I1
10 I1 + 5 I2 = E2-E1 =6.35 - 3.9 = 2.45

2 I1 + I2= .49............................EQ5

3.9 +10 I1=-20 (I1-I2)
30 I1-20 I2=-3.9..........................EQ 6

SOLVING EQ 5 AND 6 WE GET

I1=(20*.49-3.9)/70 = 0.084285714 A
The direction is same as shown in the original diagram2.

I2= .49 -2(0.084285714) == 0.321428572 A
the +ve sigh indicates that it is in same as the original figure2.

I3= I1-I2 =-0.2371428A

the direction is in opposite direction as shown in figure 2

across AB
V(ab) =Va-Vb = - 5 *0.321428572 + 6.35 =4.7428571 V .........................eq 1

Across BCDA(when switch K1 closed )

V(ab) =Va-Vb = E1 +10 I1 = 3.9+10*0.084285714 =4.7428571V................................eq2

when switch K1 open

Vab = 0

Across BFGA(when switch K1 closed )

V(ab) =Va-Vb = -20 I3 =-20*-0.2371428 =4.7428571V...........................................eq=3

so potential difference is SAME in all the cases..

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