Question

Determine the resistance of a certain resistor that dissipates 0.2 W when the current is 50 mA.

Select one:

a. 80 ohms

b. 0.5 k-ohms

c. 72  ohms

d. 4 ohms​

Answer 1

Answer:

80 ohms is the required answer

Explanation:

According to the Question

It is given that ,

• Power ,P = 0.2 W
• current ,I = 50mA

We need to calculate the resistance of the resistor .

Firstly we change the unit here .

Current

1mA = 1/1000

50mA = 50/1000 = 0.05 A

Now,

calculating the resistance of the resistor.

Relationship between Resistance , Power & Current .

• P = I²R

where,

P denote Power

I denote Current

R denote Resistance

Substitute the value we get

➺ 0.2 = 0.05² × R

➺ 0.2 = 0.0025 × R

➺ R = 0.2/0.0025

➺ R = 80 ohm

So, the required option is (a) 80 ohm.

Answer 2

Answer:

Given :-

• A resistor that dissipates 0.2 W when the current is 50 mA.

To Find :-

• What is the resistance.

Formula Used :-

$\clubsuit$ Power Formula :

$\mapsto \sf\boxed{\bold{\pink{P =\: I^2R}}}$

where,

• P = Power
• I = Current
• R = Resistance

Solution :-

First, we have to change the current mA to A :

$\implies \sf Current =\: 50\: mA$

$\implies \sf Current =\: \dfrac{5\cancel{0}}{100\cancel{0}}\: A\: \: \bigg\lgroup \sf\bold{\pink{1\: mA =\: \dfrac{1}{1000}\: A}}\bigg\rgroup$

$\implies \sf Current =\: \dfrac{5}{100}\: A$

$\implies \sf\bold{\purple{Current =\: 0.05\: A}}$

Now, we have to find the resistance :

Given :

$\bigstar\: \: \bf{Power =\: 0.2\: Watts}$

$\bigstar\: \: \bf{Current =\: 0.05\: Ampere}$

According to the question by using the formula we get,

$\longrightarrow \sf 0.2 =\: (0.05)^2 \times R$

$\longrightarrow \sf 0.2 =\: \bigg(\dfrac{5}{100}\bigg)^2 \times R$

$\longrightarrow \sf 0.2 =\: \dfrac{5}{100} \times \dfrac{5}{100} \times R$

$\longrightarrow \sf 0.2 =\: \dfrac{25}{10000} \times R$

$\longrightarrow \sf \dfrac{2}{10} =\: \dfrac{25}{10000} \times R$

$\longrightarrow \sf \dfrac{2}{10} =\: \dfrac{25R}{10000}$

By doing cross multiplication we get,

$\longrightarrow \sf 250R =\: 20000$

$\longrightarrow \sf R =\: \dfrac{20000}{250}$

$\longrightarrow \sf\bold{\red{R =\: 80\: ohm}}$

${\small{\bold{\underline{\therefore\: The: resistance\: of\: a\: certain\: resistor\: is\: 80\: ohm\: .}}}}$