Question

three resistors of 5 ohm, 10 ohm, 30 ohm connected in parallel to a battery of 6 volt find equivalent resistance and also current in each resistor.

Answer 1

As per the question, three resistors are connected in parallel.

$Let\ R_{1}\ ,R_{2}\ and\ R_{3}$ are the three resistors.

$Let\ R_{1} =5 ohm$

       $R_{2} =10ohm$

       $R_{3} =30ohm$

The voltage of battery V= 6 volt.

Let the equivalence resistance is R.

As these are connected in parallel, then-

                                         $\frac{1}{R} =\frac{1}{R_{1}} +\frac{1}{R_{2}} +\frac{1}{R_{3}}$

                                                             $=\frac{1}{5} +\frac{1}{10} +\frac{1}{30}$

                                                             $=\frac{6+3+1}{30}$

                                                             $=\frac{10}{30}$

                                         $Hence\ R=\frac{30}{10} \ ohm$

                                                            = 3 ohm

Now we are asked to calculate the current in each resistor.

The net current flowing through the circuit is-

                                                          $i=\frac{V}{R}$

                                                                 $=\frac{6}{3}\ A$

                                                                 $=2\ A$

The current in 5 ohm will be    $= \frac{6}{5} \ A$

                                                   =1.2 A

The current in 10 ohm will be   $=\frac{6}{10}\ A$

                                                   =0.6 A

The current in 30 ohm will be  $=\frac{6}{30}\ A$

                                                   =0.2 A

Here, A is the unit of current called ampere.

                                           

Answer 2

Answer:

Value of current in 5 ohm = 1.2A

10 ohm = 0.6A

30 ohm = 0.2A

Total current in the circuit = 2A

Effictive resistance = 3 ohm