Electricity Tutorial 5 - Energy and Power in Circuits

Conventional current goes from positive to negativeElectrons carry energy around the circuit; they go from negative to positive.  In the early days, physicists didn't know about the electron, which is why they got it all wrong.  Correction would require a complex re-write of the Laws of Physics, a task which no-one is likely to be bothered to tackle.  So all conventional currents are from positive to negative.  All currents are treated as conventional.

 

 

We can measure the energy in a circuit by measuring the voltage and the current.

 

 

The voltage current graph looks like this:

 

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:

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:

P = IV 

  

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

      

Question 1

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?

Answer

Question 2

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

Answer

 

The Heating Effect of a Current

We know that:

So we can write:

P = I × 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:

So we can write:

P = V × 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

The graph looks like this:

The graph shows that if we double the current, we get four times the power, consistent with the idea that P µ I2.  If we were to plot P against I2 we would get a straight line graph.  

Question 3

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?

Answer
Question 4

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?

Answer

 

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

This was a 33 W resistor connected to a 20 V supply.  The current would be 20 V ÷ 33 W = 0.61 A

The power would be 0.61 A × 20 V = 12 watts.  Plenty enough to fry a 1 watt resistor.

 It is important that we ensure that any current limiting resistors can dissipate the power through them.  The above situation could be highly dangerous.