VISUAL PHYSICS ONLINE

4.12 ELECTRICITY

P41 003.m

Can there exist any situation where you can have a large current using an electrical energy source which has a low emf? Justify your answer.

Consider a long extension cord attached to a 240 V electric light globe. Is most of the resistance in the wire cord, the plug or the light globe? Justify your answer.

Two incandescent 240 V light globes P and Q have equal length filaments made of the same material. The filament of light globe P is twice the diameter of light globe Q. Both globes are plugged in and turned on. Compare the brightness of the two light globes. Justify your answer.

Light globe P is rated as 240 V, 100 W. Light globe Q is rated 240 V, 75 W. Compare the brightness of the two globes. What is the resistance of each globe? When connected to a power point and tuned on, what current flows through each globe?

Two 12 V light globes P and Q have power ratings of 36 W and 5 W respectively.

(a) The two globes P and Q are connected separately to identical 12 V batteries. Which globe will be the brightest? Which light globe has the largest current through it?

(b) The two light globes are connected in series to a 12 V battery. Which globe will be the brightest? Which light globe has the largest current through it?

(c) The two light globes are connected in parallel to a 12 V battery. Which globe will be the brightest? Which light globe has the largest current through it?

Justify each answer.

When you heat water in an electric kettle, the same number of electrons enter the heater element as leave it. Also, the electrons have the same drift velocity on entering and leaving the heater element. What do we pay for - where does the energy come?

View solution below only after you have completed the answering the question.

Solution

For an ideal battery, if a very low resistance is connected to it, then a very large current would be drawn from the battery. For a real battery this will never happen. Real batteries have some internal resistance which limits the maximum current drawn from the battery. Also, the power supplied by the battery will depend upon the rate at which chemical reactions occur to maintain the potential difference across the battery terminals.

The power dissipated in a resistance is given by . The plug, cord and light globe are all connected in series, hence the same current will pass through the plug, cord and globe. We want most of the energy dissipated in the globe and not the plug or cord. Therefore, the resistance of the globe ideally should be much larger than the resistance of the plug or cord.

Light globe P has a filament which is twice the dimeter as light globe B. Therefore, light globe P will be the globe which has the smallest resistance value. We must be careful in interpreting the equation for power . Both light globes are connected to a 240 V electricity supply, so the potential difference V is constant for both globes. Therefore, we can only use the equation . So, globe P which has the smaller resistance will be the brighter globe.

Light globe P 240 V 100 W higher power à globe P brighter than globe Q

Light globe Q 240 V 75 W

We must be careful in interpreting the equation for power . Both light globes are connected to a 240 V electricity supply, so the potential difference V is constant for both globes. Therefore, we can only use the equation .

(a) Globe P has the higher power rating and will be the brighter globe.

(b) When the globes are connected in series, Q will be the brighter globe, since the same current passes through each globe and globe Q has a greater resistance than globe P.

(c) When the globes are in parallel, the same potential difference of 12 V is across each globe. The globes act independently, hence globe B is brighter than globe Q.

The energy that is dissipated in the heater element of the kettle comes from the source of electrical energy. The source of electrical energy creates an electric field within the circuit. The electrons in the heater element are acted on by an electrical force due to the electric field. Work is done on the electrons by the electric force causing them to accelerate and gain kinetic energy. However, these electrons have inelastic collisions with the atoms of the heater element and their kinetic energy is lost and absorbed as thermal energy increasing the temperature of the heater element. The electrons are again accelerated by the electric field and further collisions occur. So, the energy absorbed by the heater element originates from the electric field created by the source of electrical energy (battery or power point). The electrons are continually gaining and losing kinetic energy. However, no electrons are created or lost in the circuit. So the number of electrons entering or leaving the heater element are the same. Although the electrons are always speeding up due to the gain in kinetic energy by the work done by the electrical force acting on the electrons and slowing down due to the inelastic collisions, the electrons have the same average speed through the circuit, otherwise electrons would accumulate in parts of the circuit and in other parts of the circuit spread out.