physics help

Question

2.2. a battery having EMF of 50 volts and internal resistance of 0,3 ohms is connected in parallel with a direct-current generator of EMF 60 Volts and internal resistance of 0,4 ohms. The combination is used to supply a load having a resistance of 10,6 ohms. Use Kirchoff’s theorem to determine: 2.2.1. the value and direction of the current through the battery 2.2.2. the value and direction of the current through the generator 2.2.3. the potential difference across the load

Answer 1

Step 1:

(2.2)

A DC generator has emf of 60 V.

Internal resistance of the DC generator is 0.4 .

A battery has emf of 50 V.

Internal resistance of the battery is 0.3 .

DC generator and battery are connected in parallel to the load of 10.6 .

Draw a circuit with above specifications.

Step 2:

(2.2.1)

Find the current through generator :

Redraw the circuit with current directions and nodes.

Apply Junction rule at node b.

Apply KVL to a loop abeda.

Apply KVL to a loop bcfeb.

Substitute equation (1) in equation (2) and (3).

Step 3:

Solve the equations (4) and (5).

Add the equations (4) and (5).

Substitute  in equation (4).

Substitute in .

So the value of current through the generator is 17.2043 A.

The direction of the current is toward the node b.

Answer 2

Contd....

Step 4:

(2.2.2)

The value of current through the battery is .

So the value of current through the battery is 12.968  A.

The direction of the current is toward the node c.  (In opposite direction with respect to generator)

Step 5:

(2.2.3)

Find the terminal voltage across the load.

The current across the load is .

Use ohms law : .

Where i is current through load,

           R is resistance offered by load.

The voltage across the load is 54.1395 V.

Solution:

(2.2.1)

The value of current through the generator is 17.2043 A.

The direction of the current is toward the node b.

(2.2.2)

The value of current through the battery is 12.968  A.

The direction of the current is toward the node c.

(2.2.3)

The voltage across the load is 54.1395 V.