Question

Three resistors of 5 ohm 10 ohm and 20 ohm respectively are connected to a battery of 12 volt as shown in circuit given below:
Calculate:
(A) current through each resistor
(B) total current in the circuit
(C) total resistance of the circuit

Answer 1

Given:

• Three resistors of 5 ohm 10 ohm and 20 ohm respectively are connected to a battery of 12 volt.

To Find:

      (A) current through each resistor

      (B) total current in the circuit

      (C) total resistance of the circuit

Solution:

   $V=12V$

$5 \Omega, 20 \Omega$ are connected in parallel.

(a) Current through $5 \Omega$

                              $= \frac{V}{R}$  

                              $= \frac{12}{5} = 2.4 A$

    Current through $20 \Omega$  $= \frac{V}{R} = \frac{12}{20} = 0.6 A$

    Current through $10\Omega = \frac{V}{R} = \frac{12}{10} = 1.2 A$

(b) Total current in the circuit $= 2.4 + 0.6 + 1.2 = 4.2 A$

(c)  Total resistance in the circuit=R

    $5 \Omega, 20 \Omega$ are connected in parallel.

         $R = 10 + \frac{5 \times 20 }{5+20}$

        $R = 10 + \frac{100 }{25}$

       $R = 10 + 4$

       $R = 14 \Omega$

Thus, The Total resistance in the circuit $R = 14 \Omega$