Question

Two resistors x and y are connected in series with a source voltage of 24V. X is having a resistance of 8 ohm and the voltage drop across the Y resistor is 12V. Find the current in the circuit and the resistance of Y.

Answer 1

Given :

The given two resistors  X and Y are connected in series .

Voltage of source through which these two resistors are connected = 24 V

Resistance of X = 8 ohm

Voltage drop across the resistor Y = 12 V

To Find :

Value of current i the circuit and the resistance of Y  =?

Solution :

Since the two resistances are connected in series , so the equivalent resistance will be the sum of resistances of them .

So $R_{eqv} = R_X + R_Y$

             =($8 + R_Y$) ohm

Now using Ohm's Law Current through the circuit can be given as :

$I = \frac{V}{R_{eqv}}$

  = $\frac{24}{8 + R_Y}$

Now the voltage drop across Y will be :

$V_Y = I \times R_Y$

Or, $12 = \frac{24}{8 + R_Y} \times R_Y$

Or,$8 + R_Y = 2 \times R_Y$

Or, $R_Y = 8$ ohm

Now the current through the circuit is :

$I = \frac{24}{8 + 8}$

  = $\frac{24}{16}$

  = 1.5 A

Hence the current through the circuit is 1.5 A and the resistance of Y is 8 ohm .