Question

How many 330 ohms resistors in parallel are required to carry 20 Amperes on a 220 Volt line??

Answer 1

Given :

⟶ Resistance of resistor = 330Ω

⟶ Current flow in circuit = 20A

⟶ Voltage of battery = 220V

To Find :

➠ No. of resistors in parallel connection.

SoluTion :

➳ As per ohm's law, current flow in a conductor is directly proportional to the applied potential difference.

Mathematically, V = IR

✴ Eq. resistance of parallel connection :

⇒ V = I × Req

⇒ 220 = 20 × Req

⇒ Req = 220/20

⇒ Req = 11Ω

✴ No. of resistors in parallel :

➺ 1/Req = 1/R1 + 1/R2 + ... + 1/Rn

[R1 = R2 = ....... = Rn = R ]

➺ 1/Req = 1/R + 1/R + ... + 1/R

➺ 1/Req = n/R

➺ Req = R/n

➺ 11 = 330/n

➺ n = 330/11

➺ n = 30

Answer 2

$\bf \huge \green{answer \: }$

$\bf { \underline{ \underline{ \red{To \: solve \: this \: question, \: you \: have \: to \: make \: 2 \: equations \: for \: Resistance \: R}}}}$

Let the total number of resistors required is n.

So, total resistance of the circuit would be:

1/R= 1/330+1/330+1/330.....n times

1/R= n/330

R= 330/n.......equation 1

According to Ohm's law,

V=IR

R=V/I

We have V=220, I= 20

Thus, total resistance R= 220/20

R= 11......equation 2

From 1 and 2, we get

330/n = 11

n= 330/11 = 30

$\rm \bold{ \underline { \underline{\blue{</p><p>Thus, we \: need \: 30 \: resistors \: of \: 330 \: ohms \: to \: connect \: in \: parallel \: in \: the \: circuit}}}}$