Using Thevenin’s
theorem, calculate the p.d. across terminals A and B in figure 14 below.
theorem, calculate the p.d. across terminals A and B in figure 14 below.
Finding Vth
Disconnect the
7Ω resistor connected to terminals A and B to get a circuit as shown in figure
15 below.
7Ω resistor connected to terminals A and B to get a circuit as shown in figure
15 below.
Obviously, there
is no current through the 1Ω resistor and hence no voltage drop across it.
Therefore VAB = VCD = Vth. As seen, current
(I) flow due to the combined action of the two batteries. Net voltage in the
CDEF circuit = 18 – 6 = 12V. (Please take note of the polarities of the
batteries).
is no current through the 1Ω resistor and hence no voltage drop across it.
Therefore VAB = VCD = Vth. As seen, current
(I) flow due to the combined action of the two batteries. Net voltage in the
CDEF circuit = 18 – 6 = 12V. (Please take note of the polarities of the
batteries).
Total resistance
= 6 + 3 = 9Ω
= 6 + 3 = 9Ω
Hence I = 12/9 =
1.33A
1.33A
VCD =
6V + Voltage drop across 3Ω resistor
6V + Voltage drop across 3Ω resistor
= 6V + (1.33 x 3)
= 6 + 3.99
= 9.99V
Vth =
VCD = 9.99V ≈ 10V.
VCD = 9.99V ≈ 10V.
Finding Rth
Short circuit
the two batteries, since their internal resistances are not stated, they are
assumed to be zero and redraw the circuit as shown in figure 16 below.
the two batteries, since their internal resistances are not stated, they are
assumed to be zero and redraw the circuit as shown in figure 16 below.
From figure 16
above,
above,
Rth =
1 + (6||3)
1 + (6||3)
= 1 + (6 x 3)/(6 + 3)
= 1 + 2 = 3Ω
The Thevenin’s
equivalent circuit is shown in figure 17 below with the 7Ω resistor reconnected
back into the terminals A and B.
equivalent circuit is shown in figure 17 below with the 7Ω resistor reconnected
back into the terminals A and B.
The potential
difference across the 7Ω resistor can be found using the proportional voltage
formula.
difference across the 7Ω resistor can be found using the proportional voltage
formula.
P.d. across A and
B = 10 x 7/(7 + 3) = 7V.
B = 10 x 7/(7 + 3) = 7V.
