Question

2.8MJ of energy are used when 0.80 A of current pass through a 4500Ω resistor. How

many electrons are responsible for this?

Answer 1

So, the number of electron that moving in a conductor approximately
`\sf{\bold{4.85 \cdot 10^(21)}}` electrons.

Introduction and Formula Used

Hi! Here I will help you to solve problems related to the relationship between electrical energy and the number of electron moving in a conductor (especially wire). The relationship between electrical energy and the number of electrons is mediated by the charge possessed by the electrons themselves with the value approximately
`\sf{1 \: e = 1,602 \cdot 10^(-19) \: C}`. So that, the relationship between charge and the amount of electron that moving in a conductor can be expressed by the following equation:

`\boxed{\sf{\bold{Q = N \cdot e}}}` ... (1)

With the following condition:

• Q = charge in a conductor (C)
• N = the number of electron that moving in a conductor
• e = the value of the charge possessed by each electron (C)

Then, we will count the electrical energy (E) from amount of charge and voltage with
`\bold{\sf{E = Q \cdot V}}`. Remember that,
`\bold{\sf{V = I \cdot R}}`. So, we can conclude that the relationship between electrical energy with number of electron, electricity current, and the resistance of a conductor can be expressed by the following equation:

`\boxed{\sf{\bold{E = N \cdot e \cdot I \cdot R}}}` ... (2)

With the following condition:

• E = the value of electrical energy (J)
• I = the value of electricity current (A)
• R = the resistance in a conductor (
  `\varOmega`)

Problem Solving

We know that:

• E = the value of electrical energy = 2,8 MJ =
  `\sf{2,8 \cdot 10^6}` J
• I = the value of electricity current = 0.80 A
• R = the resistance in a conductor =
  `\sf{4,5 \cdot 10^3 \: \varOmega}`
• e = the value of the charge possessed by each electron =
  `\sf{1,602 \cdot 10^(-19) \: C}`

What was asked?

• N = the number of electron that moving in a conductor = ... ?

Step by step:

`\sf{\bold{E = N \cdot e \cdot I \cdot R}}`

`\sf{2,8 \cdot 10^6 = N \cdot 1,602 \cdot 10^(-19) \cdot 0.80 \cdot 4,5 \cdot 10^3}`

`\sf{2,8 \cdot 10^6 = N \cdot 5,77 \cdot 10^(-19+3)}`

`\sf{2,8 \cdot 10^6 = N \cdot 5,77 \cdot 10^(-16)}`

`\sf{N = (2,8 \cdot 10^6)/(5,77 \cdot 10^(-16))}`

`\sf{N \approx 0.485 \cdot 10^(6-(-16))}`

`\sf{N \approx 4.85 \cdot 10^(22-1)}`

`\sf{\bold{\therefore N \approx 4.85 \cdot 10^(21)}}` electrons

Conclusion

So, the number of electron that moving in a conductor approximately
`\sf{\bold{4.85 \cdot 10^(21)}}` electrons.

Answer 2

Okay, let's break this down step-by-step:

Given:

Energy (E) = 2.8 MJ

Current (I) = 0.80 A

Resistance (R) = 4500 Ω

We can use the equation:

E = I2Rt

Where:

E is energy in Joules (J)

I is current in Amps (A)

R is resistance in Ohms (Ω)

t is time in seconds (s)

Let's first calculate the time (t):

E = I2Rt

2.8 x 106 J = (0.80 A)2 x 4500 Ω x t

t = 2.8 x 106 J / (0.80 A)2 / 4500 Ω

t = 1000 s

Now we know the time is 1000 s.

Next, we can calculate the number of electrons (n) using the equation:

n = It/q

Where:

I is the current in Amps

t is the time in seconds

q is the charge of an electron (1.60 x 10-19 C)

Plugging in the values:

n = It/q

n = (0.80 A)(1000 s)/(1.60 x 10-19 C)

n = 5 x 1018 electrons

Therefore, the number of electrons responsible for transferring the 2.8 MJ of energy is 5 x 1018 electrons.

In summary:

- Used the equations for energy, current and charge to calculate the number of electrons

- Determined the time (t) first, then calculated the number of electrons (n)

- The number of electrons is 5 x 1018

Let me know if you need any clarification or have additional questions! I'm happy to explain my working in more detail.