Question

Since the Christmas season is approaching, a shopping mall owner decides to decorate his mall with the decorative elements as shown in the following

circuit. The values of the resistances offered by different decorative stars are as follows: the resistance offered by red star is 8 ohms, blue star offers a

resistance of 6 ohms, while the pink star offers resistance of 5 ohms and the green star has a resistance of 10 ohms. The owner decides to simply his circuit,

in this regard, find the Thevenin's equivalent across the green star and also determine the current that will flow across the green star

Answer 1

Kindly note the circuit referred to is missing

Adjusting the condition of the question the circuit (Figure 1) below is introduced

The green $($ 10$\Omega)$ is opened as in figure two below

Current through Red and Blue in the open circuit

$I= \frac{49}{6+8}=3.5A$

Voltage across Blue

$=3.5×6$

$=21V$

This is the Thevenin's voltage

$V_{TH}=21V$

The current source is open as show in figure 3 below

The open circuit resistance is

$= 5\Omega$ in series with $6\Omega$ and $8\Omega$ in parallel

This is Thevenin's resistance

$R_{TH}=5+\frac{6×8}{6+8}$

$=8.43\Omega$

Figure 4 is the equivalent the Thevenin circuit.

Current through Green

$\Iota_G=\frac{21}{8.43+10}=1.14A$