electrical circuiting physics

Question

A 12V battery of internal resistance 5 ohm is connected in parallel with a 10V batter of internal resistance 3 ohm to a load of 30 ohm. Use thvenins theorem to calculate the current through the load.

Answer 1

Step 1:

Two cells are connected in the parallel.

The emf of the first cell is 10 V.

The internal resistance of the first cell is 3 .

The emf of the second cell is 12 V.

The internal resistance of the second cell is 5 .

Load resistance is  30 .

Draw a circuit with above specifications :

Step 2:

Find the current through the load.

 Thevenin's Theorem :

Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load.

Now reduce the circuit to a equivalent Thevenin's 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.

3Ω Resistor in parallel with the 5Ω Resistor .

So thevenin's resistance

Step 3:

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 .

 

So the voltage drop across the 30 Ω resistor can be calculated as:

Step 4:

Therefore the Thevenin's Equivalent circuit is shown below with the 30 Ω resistor connected.

 

Current flowing in the circuit is :

The current flowing through the load is 0.337 A .

Solution:

The current flowing through the load is 0.337 A .