Question

Find the power, given energy E = 2J and
current density J = x2 varies from x = 0
and x = 1.
Select one:
A. 43894
O B. 43892
O C. 1/3
0 D. 1​

Answer 1

Power = 2/3 units

Explanation:

There is an error in the question with the options given. Please find the full question and solution below.

Find the power, given energy E = 2J and current density J = x2 varies from x = 0 and x = 1.

a) 1/3

b) 2/3

c) 1

d) 4/3

Solution:

From Stoke’s theorem, we know that Power P can calculated using the product of E * I = ∫ E. J ds

P = ∫2 x² dx where x = 0 -> 1.

 = 2 ∫x² dx where x = 0 -> 1.

 = 2 [x³/3] where x = 0 -> 1.

 = 2 [1³/3 - 0³/3]

 = 2 (1/2)

 = 2/3

So we get Power = 2/3 units.

Option B is the answer.

Answer 2

Given :  E = 2J and  current density J = x2 varies from x = 0  and x = 1.

To Find   Power

a) 1/3

b) 2/3

c) 1

d) 4/3

Solution:

energy E = 2J

current density J = x2 varies from x = 0  and x = 1

Power =  ∫ E. J ds

    $=\int\limits^1_0 {2x^2} \, dx$  

  $=2\int\limits^1_0 {x^2} \, dx$  

using integration ∫xⁿ  = xⁿ⁺¹ / (n + 1)

$=2 \left[\dfrac{x^3}{3} \right]_{0}^1$  

$=2 \left[\dfrac{1^3}{3} -\dfrac{0^3}{3} \right]_{0}^1$  

= 2 (1/3)

= 2/3

power, = 2/3

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