Question

three resistors 8 ohm 12 ohm 6 ohm are connected to 12 volt battery as shown in figure find. the current through 8 ohm resistor. the potential difference across the parallel combination of 6 ohm and 12 ohm. the current through 6 ohm resistor​

Answer 1

Given,

A circuit as shown in the figure.

To find,

a) The current through the 8-ohm resistor

b) the potential difference across the parallel combination of 6 ohms and 12 ohms

c) The current through the 6-ohm resistor

Solution,

We can simply solve this numerical problem by using the following process:

As per ohms law,

" For a voltage V across the conductor, current I flowing through the conductor and resistance R provided by the conductor to the flow of current, Voltage = Resistance × current "

{Statement-1}

Mathematically,

If a set of resistors are arranged in a series type of arrangement, then the equivalent resistance of the arrangement is equal to the total of the individual resistances. The total current across all the resistors, arranged in series type, is equal.

{Statement-2}

Similarly, if a set of resistors are arranged in a parallel type of arrangement, then the reciprocal of the equivalent resistance of the arrangement is equal to the sum of the reciprocals of the individual resistances. The total voltage supply across all the resistors, arranged in parallel type, is equal.{Statement-3}

Now, according to the given circuit;

The 8 ohms resistor is in a series type of arrangement with the parallel type combination of the 6 ohms and 12 ohms resistor, respectively.

Let us assume that the equivalent resistance of the parallel type combination of the 6 ohms and 12 ohms resistor is r ohms.

According to statement-3;

1/r = 1/12 + 1/6 = 1/12 + 2/12 = 3/12 = 1/4

=> r = 4 ohms

The equivalent resistance of the complete circuit

= r ohms + 8 ohms

= 12 ohms

Now, according to the question;

The total resistance of the circuit = 12 ohms

Total voltage supply = 12 V

This implies, according to statement-1,

The total current flowing through the circuit

= Total voltage supply / Total resistance of the circuit

= 12 V / 12 ohms = 1 A

Now, according to statement-2 and statement-3;

The current flowing through the 8 ohms resistor and the parallel arrangement of the 6-12 ohms resistor is the same.

And, the voltage supply across the 2 resistors, arranged in parallel type, is equal.

So, the current through the 8 ohms resistor

= Total current flowing through the circuit

= 1 A (Answer - a)

Now, for the parallel arrangement of 6-12 ohms resistor;

equivalent resistance = 4 ohms

total current flowing = 1 A

So, the potential difference across the parallel combination of 6 ohms and 12 ohms

= equivalent resistance×total current flowing

= 4 ohms × 1 A

= 4 V (Answer - b)

Now, for the 6-ohm resistor;

potential difference = 4 V

So, the current through the 6-ohm resistor

= potential difference/resistance

= 4 V / 6 ohms

= 0.67 A (Answer - c)

Hence, the current through the 8 ohms resistor is equal to 1 A, the potential difference across the parallel combination of 6 ohms and 12 ohms is equal to 4 V, and the current through the 6 ohm resistor is equal to 0.67 A, respectively.