Question

When a current of 4.0 A passes through a certain resistor for 10 minutes, 2.88 * 10 J of heat are produced .
Calculate :- a) the power of the resistor
b) the voltage across the resistor

Answer 1

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When a current of 4.0 A passes through a certain resistor for 10 minutes, 2.88 × 10⁴ J of heat are produced .

Calculate :-

a) the power of the resistor

b) the voltage across the resistor

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Let us write the given data first and then solve

GIVEN:

Current (I) = 4 Ampere

Time (T) = 10 minutes

Energy (H) = 2.88 × 10⁴ J

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SOLUTION:

Time is given in minutes it should be converted to seconds

T = 10 $\times$ 60 = 600 sec

$\pink{ \boxed{A.) \: Power\: of \:the \:Resistor }}$

➠ H = I²RT

➠ 28800 = 4²×R×600

➠ $\dfrac{28800}{16\times 600} = R$

➠ $\dfrac{288\cancel 0\cancel 0}{16\times 6\cancel 0\cancel 0} = R$

➠ $\dfrac{288}{16\times 6 } = R$

➠  $\dfrac{288}{ 96 } = R$

➠ 3 = R

R = 3Ω is the resistance we need to calculate power

We know that

P = I² R

= 4² x 3

P = 48 W

Hence 48W is the power of the given resistor

$\pink{ \boxed{B.)\: Voltage\:across \: the\: resistor }}$

➠  V = I R

➠ V = $4 \times 3$

➠ V = 12 Volt

Hence 12 V is voltage of the given resistor

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To calculate power resistance of any problems use these formulas

✧ H = I²RT

✧ V = IR

✧ P = I² R  or P = $\dfrac{W}{Δt}$

Using these formulas it is easy to calculate

ℌope ℑt ℌelps

Thanks for asking