Question

the total power consumed by the network shown in the figure is 16 W. find the value of 'R' and the total current.​

Answer 1

Given,

The total power consumed by the network shown in the figure = 16 W

To find,

The value of R.

Solution,

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

Mathematically,

Power (P) = voltage (V) x electric current (I) {Equation-1}

Also, as per ohms law,

Voltage (V) = Resistance x electric current (I)

=> electric current (I) = Voltage (V) / Resistance

electric current (I) = Voltage (V) / Resistance{Equation 2}

From equations 1 and 2, we get;

Power (P) = voltage (V) x Voltage (V) / Resistance

=> total resistance = V^2/P

Now, according to the question;

The total resistance of the circuit

= V^2/P

= (8x8)/16 ohms

= 4 ohms

Now, 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. 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.

Now, according to the question;

The total resistance of the circuit

= {(1/4) + (1/R)}^-1 + {(1/2) + (1/8)}^-1

=> {(1/4) + (1/R)}^-1 + 8/5 ohms= 4 ohms

=> {(1/4) + (1/R)}^-1 = 4 - 8/5 = 12/5

=> (1/4) + (1/R) = 5/12

=> 1/R = 5/12 - 1/4 = 2/12 = 1/6

=> R = 6 ohms

Hence, the value of R is equal to 6 ohms.