help solving q2

Question

2. Use thevenin’s theorem to determine current through R4 resistor in the circuit diagram shown.

 

Answer 1

Step 1:

Find the current through the resistance R4.

 Thevenins Theorem :

Thevenins Theorem states that it is possible to simplify any linear circuit, to an equivalent circuit with just a single voltage source and series resistance connected to a load.

Now reduce the circuit to a equivalent Thevenins circuit .

Find the Equivalent Resistance (Rs):

Find the Thevenin resistance by removing all power sources in the original circuit (voltage sources shorted and current sources open) and calculating total resistance between the open connection points.

6Ω Resistor in parallel with the 20Ω Resistor .

Now the resistance in series with 5Ω Resistor .

So thevenins resistance

Step 2:

Find the Equivalent Voltage (Vs):

Find the Thevenin source voltage by removing the load resistor from the original circuit and calculating voltage across the open connection points where the load resistor used to be.

Apply KVL to the above circuit .

  (The current in the second loop is zero since it is kept open )

So the voltage drop across the 20 Ω resistor can be calculated as:

Step 3:

Therefore the Thevenins Equivalent circuit is shown below with the 15 Ω resistor connected.

The current across the load is

Solution :

The current across 15  Ω resistor is 0.3124 A.