Question

How many 176ohm resistors ( in parallel ) are required to carry 5A on a 220V line​

Answer 1

Given :-

• Resistors are connected in parallel.

• Resistance of one resistor, R = 176Ω

• Current, I = 5A

• Voltage, V = 220V

To Find :-

• Number of resistors in parallel connection.

Solution :-

Let the number of resistors be n.

According to ohm's law :-

$: \implies \sf V= IR_{eq}$

$: \implies \sf 220= 5R_{eq{$

$: \implies \sf R_{eq} = \dfrac{220}{4}$

$: \implies \sf R_{eq} = 44 \Omega$

Equivalent resistance in parallel :-

$\bf \dag\underline{\boxed{\bf \dfrac{1}{R_{eq}}= \dfrac{1}{R_1}+\dfrac{1}{R_2}+.............................. \dfrac{1}{R_n} }}$

Here resistance of all resistors are same.

So,

$\underline{\boxed{\bf\dfrac{1}{ R_{eq}}= n \times \dfrac{1}{R}} }$

$: \implies\sf \dfrac{1}{44} = n \times \dfrac{1}{176}$

$: \implies\sf176 = n \times 44$

$: \implies\sf n = \dfrac{176}{44}$

$: \implies\sf n = 4$

Number of resistors in parallel :- 4

Answer 2

Answer:

Given :-

Resistors are connected in parallel.

Resistance of one resistor, R = 176Ω

Current, I = 5A

Voltage, V = 220V

To Find :-

Number of resistors in parallel connection.

Solution :-

Let the number of resistors be n.

According to ohm's law :-

Number of resistors in parallel :- 4