Question

A resistor produces 200 j of heat every second when connected with a source of 220 volts. find its resistance and the current that will pass through it

Answer 1

$\bigstar$ Answer $\bigstar$

Given:

A resistor produces 200 J of heat every second

Connected with a source of 220 Volts

To Find:

It's Resistance and the Current

Solution:

We know that,

$\implies \rm W=I^{2}Rt$

$\rm Using, \ \ I=\dfrac{V}{R} \\\\ We \ get,$

$\implies \rm W=\dfrac{V^{2}t}{R}$

When, Work is dissipated in the form of Heat.

H = W

Therefore,

$\red{\implies \rm H=\dfrac{V^{2}t}{R}}$

Given that,

H = 200 Joules

V = 220 Volts

t = 1 second

According to the Question,

We are asked to find it's Resistance

Therefore,

$\implies \rm R=\dfrac{V^{2}t}{H}$

Substituting above values,

We get,

$\implies \rm R=\dfrac{(220)^{2} \times 1}{200}$

$\implies \rm R=\dfrac{48400}{200} \ \Omega$

$\pink{\implies \rm R=242 \ \Omega}$

According to the Question,

We are also asked to find the current that will pass through it

Hence,

Using Ohm's Law

$\green{\boxed{\rm V=IR}}$

To find current ($\rm I$)

$\orange{\implies \rm I=\dfrac{V}{R}}$

Given that,

V = 220 Volts

And, We found out that,

R = 242 Ω

Substituting above values,

We get,

$\implies \rm I=\dfrac{220}{242} \ A$

$\blue{\rm \implies I = 0.9 \ A}$