In figure 6 below, compute the relative potentials of points
A, B, C, D and E when (i) Point A is grounded and (ii) point D is grounded.
Does it affect the circuit operation or potential difference between any pairs
of points?
A, B, C, D and E when (i) Point A is grounded and (ii) point D is grounded.
Does it affect the circuit operation or potential difference between any pairs
of points?
Solution
As seen from figure 6 above, the two batteries have been
connected in series opposition. Hence, net circuit voltage = 34 – 10 = 24V.
connected in series opposition. Hence, net circuit voltage = 34 – 10 = 24V.
Total circuit resistance = 6 + 4 + 2 = 12Ω
Hence, circuit current = 24/12 = 2A
Drop across 2Ω resistor = 2 x 2 = 4V
Drop across 4Ω resistor = 2 x 4 = 8V
Drop across 6Ω resistor = 2 x 6 = 12V
(i)When point A is grounded
Since point B is directly connected to the positive terminal
of the battery whose negative terminal is earthed, VB = 34 – 4 =
30V.
of the battery whose negative terminal is earthed, VB = 34 – 4 =
30V.
As we go from point C to D i.e. from positive terminal of 10V
battery to its negative terminal, there is a decrease in potential of 10V.
Hence VD = 30 – 10 = 20V i.e. point D is 20V above the ground A.
battery to its negative terminal, there is a decrease in potential of 10V.
Hence VD = 30 – 10 = 20V i.e. point D is 20V above the ground A.
Similarly, VE = VD – Voltage fall across
4Ω resistor = 20 – 8 = +12V.
4Ω resistor = 20 – 8 = +12V.
Also VA = VE – fall across 6Ω resistor =
12 – (2 x 6) = 0V.
12 – (2 x 6) = 0V.
(ii)When point D is grounded.
Starting from point D, as we go to E, there is a fall of 8V.
Hence, VE = -8V.
Hence, VE = -8V.
Similarly, VA = – (8 + 12) = -20V.
As we go from A to B, there is a sudden increase of 34V
because we are going from a negative terminal of the battery to its positive
terminal.
because we are going from a negative terminal of the battery to its positive
terminal.
VB = -20 + 34 = +14V
VC = VB – voltage fall across 2Ω
resistor = 14 – 4 = +10V.
resistor = 14 – 4 = +10V.
It should be so because C is connected directly to the
positive terminal of the 10V battery.
positive terminal of the 10V battery.
Choice of the reference point does not in any way affect the
operation of the circuit. Moreover, it also does not change the voltage across
any resistor or between any pair of points (as shown below0 because the ground
current ig =0.
operation of the circuit. Moreover, it also does not change the voltage across
any resistor or between any pair of points (as shown below0 because the ground
current ig =0.
Reference Point A
VCA = VC –VA = 30-0 =+30V
VCE = VC –VE = 30-12 =+18V
VBD = VB –VD = 34-20 =+14V
Reference Point D
VCA = VC –VA = 10-(-20) =+30V
VCE = VC –VE = 10-(-8) =+18V
VBD = VB –VD = 14-0 =+14V
