alculate the potential difference

Question

Two series circuits with branches of 6ohms and 4ohms and 10ohms and 5ohms respectively are connected in parellel across a battery which has an emf 25V and an internal resistance of 0.25ohms. Calculate the potential difference across each of the extenal resistors.

Answer 1

Step 1 :

The emf of the battery is 25 V.

The internal resistance of the battery is .

Two series circuits with branches of connected in parallel.

Draw a circuit with above specifications :

 

Step 2 :

Find the equivalent resistance :

Resistors are in series.

Let is equivalent resistance of .

Resistors are in series.

Let is equivalent resistance of .

Let is equivalent resistance of .

Now is in series with the internal resistance of the battery.

Step 3 :

Find the current in the circuit :

From ohms law : .

Substitute in above formula.

Step 4 :

Apply Kirchhoffs current law (KCL) at each node :

Apply Kirchhoffs voltage law (KVL) to first loop :

Substitute in equation (1).

Answer 2

Contd.....

Step 5 :

The potential difference across the external resistor is .

Substitute and in above equation.

The potential difference across the external resistor is .

Substitute and in above equation.

The potential difference across the external resistor is .

Substitute and in above equation.

The potential difference across the external resistor is .

Substitute and in above equation.

Solution :

The potential difference across resistor is .

The potential difference across resistor is .

The potential difference across resistor is .

The potential difference across resistor is .