Electricity without the tears by Durkan Colm

Author:Durkan, Colm [Durkan, Colm]
Language: eng
Format: epub
Published: 2017-07-03T16:00:00+00:00

Solution . (i) The resistances of the battery and the bulb are in series, so the total resistance of the circuit is the resistance of the bulb plus the internal resistance of the battery, or R total = R bulb + 1 Ohm. From Ohm’s law, we can then say that , which means that R bulb = 9 Ohm.

​ (ii) All components have the same current flowing through them, so the power dissipated in the bulb is given by V bulb xI . Now, at the moment, we don’t know how much voltage is dropped across the bulb, but we do know that of the 9V we started with, some is dropped across the internal resistance of the battery, and the rest is dropped across the bulb. From Ohm’s law, V bulb = I xR bulb . We can combine all of this to give us:

P bulb = V bulb x I = (I x Rbulb) x I = I 2 x R bulb .

Plugging in the numbers from above, we find the amount of power dissipated in the bulb is = 7.29W.

​ (iii) Using the same idea as in part (ii), we can say that

P battery = V battery x I = (I x Rbattery) x I = I 2 x R battery

Now using the numbers from above, we find the amount of power dissipated in the battery is = 0.81W.

​ (iv) The total amount of power dissipated is due to both the bulb and the internal resistance of the battery, so is just the sum of the two numbers above, i.e.

)

= (0.9A)2 ☐ (9 ☐ + 8 ☐ ) = 8.1W

Is this a lot? Well, it’s not much, given that a typical kettle is 1.5 kW (1,500 Watts). We also note that the effect of the internal resistance of the battery is that the overall amount of current is reduced, and as a consequence, so is the power that is dissipated in the circuit.

Related issues

When we talk about power being dissipated in a resistor, what do we mean by that? Well, the word dissipated normally means used up, or lost. In physics it has a more specific meaning which is the loss of energy through conversion to heat. Therefore, when we pass a current through anything with resistance, it heats up, and in line with conservation of energy, the amount of energy “lost” in the resistor is the same as the potential difference between the terminals of the battery.

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