Topic 1. Charge, Current, and Potential Difference

Current and Charge

The base electrical quantity is current, the flow of charge.  All other electrical quantities are derived from it.  Current is measured in ampères, or amps (A).  Charge is measured in coulombs (C), which is defined as:

1 coulomb is the quantity of charge carried past a given point if a steady current of 1 amp flows for 1 second.

1 electron carries a charge of 1.6 ´ 10^-19 C

1 coulomb is equivalent to 6.2 ´10¹⁸ electrons.  It is much more convenient to use this rather than counting individual electrons.  You would buy a 1 kg bag of sugar rather than counting all the crystals in it.

Question 1 What do you think an electron is?

Charge and current are linked by a simple formula:

            Charge (C) = current (A) ´ time (s)

  In the syllabus the formula is written in physics code as:

  The symbol D is Delta, a Greek capital letter D, meaning “change in”.

  There are some important multipliers for current:

• 1 microamp (1 mA) = 1 ´ 10^-6 A
• 1 milliamp (mA) = 1 ´ 10^-3 A

  These are useful when we are dealing with small currents.  However we must remember to convert to SI units for doing calculations.  Watch out for this bear trap!

Question 2  Can you show that 1 coulomb is 6.2 ´10¹⁸ electrons?

Question 3  A charge of 1.24 C flows in a period of 0.63 s.  What is the current?   

Potential Difference

Potential Difference is defined as energy per unit charge.

  The unit of potential difference is the volt (V).  Using the definition, we can define the volt as Joules per Coulomb.  1 V = 1 JC^-1.

Potential difference (V) = energy converted (J)

                                                Charge (C)

In physics code we write:

Potential difference is often referred to as voltage.

Question 4  A cordless drill operates using a 14.4 V battery pack.  The battery is rated at 2 amp hours which means that it can deliver a current of two amps for a period of 1 hour.  How much energy is held by the battery?

Resistance in a wire is the opposition of a wire to the flow of electricity.  It is caused by collisions between the electrons and the atoms in the wire.  The hotter the wire, the more chance there is of a collision.  Therefore hot wires have more resistance.  The formula for resistance is:

Resistance (ohms) = potential difference (volts)

                                 current (amps)

In physics code we write this as R = V/I

The unit for resistance is ohm (W).  (The curious symbol ‘W’ is Omega, a Greek capital letter long Ō.)

Question 5 What do you understand by the term resistance?

Question 6 Use the circuit below to answer the questions:

  Watch out for bear traps in electrical calculations:

Energy and Power in Circuits

Suppose a current I flows for t seconds in a component. The charge that flowed led to E joules being dissipated in the component.

We know that:

• Q = It
• E = QV

So if we substitute Q out of the second equation, we get:

E = ItV

Now

                        Power = energy

                                       time

So we can write:

                        P = ItV

                               t

It doesn’t take a genius to see that the term t cancels out to leave us with:

Power is measured in watts (W).  1 watt = 1 joule per second

Question 7 A 12 volt heater takes a current of 3.6 A.  It is left to heat up an aluminium block for a period of 45 minutes.  How much heat energy is transferred to the aluminium block?

Question 8   What current is consumed by a 60 W light bulb operating on the 230 V mains?

The Heating Effect of a Current

We know that:

• V = IR
• P = IV

So we can write:

P = I x IR

So it doesn’t take a genius to see that by substituting the second equation into the first, we get:

P = I²R

We can use a similar method to see how voltage, resistance and power are related

We know that:

• I = V/R
• P = IV

So we can write:

P = V x V/R

So it doesn’t take a genius to see that by substituting the second equation into the first, we get:

P = V²/R

Question 9 A resistor of value 50 ohms is rated at 1 watt.  This means that if it has to give out more power than 1 watt, it will start to get hot.  What is the maximum current that it can handle?

Question 10 The same resistor as in Q 9 is then connected to a 20 volt supply.  What power will it dissipate now?  What do you think will happen to the resistor?

The picture shows the heating effect of a current on a resistor!