Question

The energy through an element is defined by W(t)=20t⁴+18t+1. The voltage required to move 3 coulombs of charge in 2 seconds is

i) 119 volts
ii) 65.67 volts
iii) 225 volts
iv) 357 volts

Answer 1

The voltage required to move 3 coulombs of charge in 2 seconds is 357 volts.

Step-by-step explanation:

To find the voltage required to move 3 coulombs of charge in 2 seconds, we need to calculate the energy using the formula E = qV, where E is the energy, q is the charge, and V is the voltage. In this case, q = 3 C and the time t = 2 s. Substituting these values into the given equation W(t) = 20t⁴ + 18t + 1, we can solve for V.

First, calculate the energy E using the formula E = qV:

E = (3 C)(V)

Next, substitute the equation W(t) = 20t⁴ + 18t + 1 into the equation E = qV:

20t⁴ + 18t + 1 = 3(V)

Now, solve for V:

V = (20t⁴ + 18t + 1) / 3

Plugging in t = 2:

V = (20(2)⁴ + 18(2) + 1) / 3

V = (320 + 36 + 1) / 3

V = 357 volts