Question

How many 176ohm resistors(in parallel) are required to carry a current of 5A in 220V line??

Answer 1

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Let the total no. of resistors = x

Given,

I = 5 A

V = 220 V

According to Ohm’s law,

V = IR

R = V/ I = 220/5 = 44Ω

Now for x number of resistors of resistance 176 Ω, the equivalent resistance of the resistors connected in parallel is 44 Ω.

1/44 = 1/176 + 1/176 + 1/176 .....χ times

1/44 = x / 176

=> x = 176/ 44

=> x = 4

Therefore, 4 resistors of 176 Ω are required to draw the given amount of current.

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Answer 2

4 resistors(in parallel) of 176 ohm are required to carry current of 5A in the 220 V.

Given: 1)Resistor of 176 ohm.

           2)Current (I) = 5 A.

           3)potential difference= 220V

To Find: Number of resistors (x)

Solution:

Resistance in parallel: When a number of resistors are connected in parallel, then the potential difference across each of them will be the same.

• If n number of resistors R₁, R₂, R₃ ..... , Rₙ are connected in parallel, the equivalent resistance is given by,

                       $\frac{1}{Rp}$=$\frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} + .... + \frac{1}{Rn}$

• Hence, when a number of resistors are connected in parallel, the reciprocal of equivalent resistance is equal to the sum of reciprocals of individual resistances.

Now, Let's say x be the number of resistors of the resistance 176 ohm, connected in parallel.

now, by using ohm's law to calculate equivalent resistance,

  ohm's law can be defined as, as long as the physical state of the  conductor remains the  same, the electric current flowing through a given conductor is directly proportional to the  potential difference applied across.

  ∴  I ∝V

       V=IR  .. (1)

substituting the given values, we get,

    $R=\frac{V}{I}$

   $R= \frac{220}{5}$  

   R= 44 ohm .

Now, we got equivalent resistance is 44 ohm and such x  resistors of 176 ohm are connected in parallel.

∴            $\frac{1}{Rp}$= $\frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} + .... + \frac{1}{Rn}$

             $\frac{1}{44} = \frac{1}{176} + \frac{1}{176} +............ + x times$

             $\frac{176}{44} = x$

           $x = 4$.

    Hence,  4 resistors(in parallel) of 176 ohm are required to carry a current of 5A in the 220 V.

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