Calculate the value of R
which will absorb maximum power from the circuit of figure 34 shown below.
Also, compute the value of the maximum power.
which will absorb maximum power from the circuit of figure 34 shown below.
Also, compute the value of the maximum power.
Solution
To find the power, it is
essential to know both I and R. Hence it is essential to find an equation
relating I to R.
essential to know both I and R. Hence it is essential to find an equation
relating I to R.
Let us remove R and find
Thevenin’s Voltage Vth across A and B as shown in figure 35 below.
Thevenin’s Voltage Vth across A and B as shown in figure 35 below.
It would be helpful to
convert the 120V, 10Ω source into a constant source as
shown in figure 36 below.
convert the 120V, 10Ω source into a constant source as
shown in figure 36 below.
Now, to find Ri or
Rth, disconnect the two current sources in figure 36 above to get a
circuit as shown in figure 37 below.
Rth, disconnect the two current sources in figure 36 above to get a
circuit as shown in figure 37 below.
Hence, Ri = Rth
= 10||5 = 3.33Ω. The Thevenin’s equivalent circuit of
the network is shown in figure 38 below.
= 10||5 = 3.33Ω. The Thevenin’s equivalent circuit of
the network is shown in figure 38 below.
According to maximum power
transfer theorem, R will absorb maximum power when it equals 3.33Ω. In that case I = 60/2Rth
transfer theorem, R will absorb maximum power when it equals 3.33Ω. In that case I = 60/2Rth
I = 60/6.66 = 9A
Pmax
= I2 R
= I2 R
= 92 x 3.33
= 270 W
