(6)

\

Step 1:

\

A resistance of $\"\"$ is connected in parallel with resistance of $\"\"$ .

\

$\"\"$

\

Find the equivalent resistance.

\

Consider $\"\"$ is the equivalent resistance.

\

$\"\"$ is connected in parallel to $\"\"$ .

\

$\"\"$

\

The equivalent resistance is $\"\"$ .

\

Step 2:

\

The equivalent resistance is connected in series with a resistance of $\"\"$ .

\

$\"\"$

\

Now find the total resistance.

\

Consider $\"\"$ is the total resistance.

\

So $\"\"$ is connected in series with $\"\"$ .

\

$\"\"$

\

The total resistance is $\"\"$ .

\

Step 3:

\

The above circuit is connected across a battery having an EMF of 18 V and an internal resistance of $\"\"$ .

\

$\"\"$

\

Now find the total equivalent resistance.

\

Consider $\"\"$ is the total equivalent resistance.

\

So $\"\"$ is connected in series with $\"\"$ .

\

$\"\"$

\

The total equivalent resistance is $\"\"$ .

\

Find the total current in the circuit.

\

Consider $\"\"$ is the total current in the circuit.

\

From ohms law : $\"\"$

\

$\"\"$ .

\

Then total current is $\"\"$

\

Substitute $\"\"$ in the total current.

\

$\"\"$

\

The total current in the circuit is $\"\"$ .

\

Step 4:

\

(6.1)

\

Find the terminal voltage of the battery.

\

Suppose that the battery with EMF $\"\"$ and internal resistance $\"\"$ supplies a current $\"\"$ through an external load resistor $\"\"$ , then the terminal voltage across the battery is $\"\"$ .

\

Substitute $\"\"$ in the terminal voltage.

\

$\"\"$

\

The terminal voltage of the battery is $\"\"$ .

\

Step 5:

\

(6.2)

\

Find the current through each resistance.

\

$\"\"$

\

The current through $\"\"$ resistance is $\"\"$ .

\

The voltage across $\"\"$ resistance is

\

$\"\"$

\

Voltage across $\"\"$ resistance is $\"\"$ .

\

Now find the voltage across the resistance $\"\"$ .

\

The terminal voltage is $\"\"$ .

\

The voltage across the resistance $\"\"$ is $\"\"$ .

\

The voltage is same in the parallel loop.

\

So voltage across the $\"\"$ and $\"\"$ is $\"\"$ .

\

Find the current $\"\"$ .

\

$\"\"$

\

Find the current $\"\"$ .

\

$\"\"$

\

Solution :

\

(6.1) The terminal voltage of the battery is $\"\"$ .

\

(6.2)

\

The current through $\"\"$ resistance is $\"\"$ .

\

The current through $\"\"$ resistance is $\"\"$ .

\

The current through $\"\"$ resistance is $\"\"$ .