Question

1. Calculate how many electrons you need to get a charge of 1 coulomb.

Answer 1

1) To make a charge of 1 Coulomb, $6.25\cdot 10^{18}$ electrons are needed

2) $3.75\cdot 10^{19}$ electrons are needed to make that current

3) The potential difference is the work done per unit charge by an electric field

4) False, false, true

Explanation:

1)

The charge of one electron is equal to (in magnitude)

$q=1.6\cdot 10^{-19}C$

This is also known as fundamental charge, and it is also indicated with the letter $e$.

The charge in this problem is

$Q=1 C$

Therefore, in order to calculate how many electrons are in 1 Coulombd of charge, we just divide the total charge by the charge of one electron:

$n=\frac{Q}{q}=\frac{1}{1.6\cdot 10^{-19}}=6.25\cdot 10^{18}$

2)

The current intensity is defined as

$I=\frac{Q}{t}$

where

Q is the charge passing through a given point of a circuit in a time interval t

In this problem, we have

t = 60 s

I = 100 mA = 0.1 A

Therefore, the charge passing through the circuit is

$Q=It=(0.1)(60)=6 C$

We know that the charge of one electron is

$q=1.6\cdot 10^{-19}C$

So the number of electrons is

$n=\frac{Q}{q}=\frac{6}{1.6\cdot 10^{-19}}=3.75\cdot 10^{19}$

3)

The electrical voltage (also called potential difference) can be understood by using the concept of energy and work.

In fact, the work done by an electric field on a charge of magnitude q is

$W=q\Delta V$ (1)

where $\Delta V$ is the potential difference between the initial and final point of motion of the charge. The potential difference is responsible for "pushing" the charge through the circuit (in particular, a positive charge is pushed towards a point of lower potential, while a negative charge is pushed towards a point of higher potential), and when this happens, the electric potential energy of the charge (due to its position in the electric field) is converted into kinetic energy (energy of motion).

So, the potential difference is basically the work done per unit charge by an electric field responsible for the acceleration of a charge, as we can rewrite eq.(1) as

$\Delta V = \frac{W}{q}$

So in this case (where the electric voltage is 5 volts), it means that the work done by this electric field per unit charge is 5 J per Coulomb of charge.

4)

False: Current is the consequence and voltage is the cause. In fact, the voltage (the potential difference between two points in the circuit) is responsible for "pushing" the charges through the circuit, and when the charges start moving, they produce a current.

False: only the battery is a source of voltage. A battery is a device that produces an electromotive force (another name for potential difference), which is responsible for "pushing" the charges through the circuit. A socket, instead, is just a device used to connect another electric device to a voltage supply.

True: an electric current can only flow in a closed circuit. When the circuit is open, in fact, there is a point in the circuit where the flow of charge is interrupted: this means that the current can no longer flow in the circuit, so there is no electric current in an open circuit.

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