1. Question of the day
How is the power used in a circuit calculated? Or: How can you tell if you should be using a ¼ W resistor or a 5 W one?

2. Energy and power in electric circuits
The box represents a circuit element with potential difference Vab = Va − Vb between its terminals and current I passing through it in the direction from a toward b.
If the potential at a is lower than at b, then there is a net transfer of energy out of the circuit element.
The time rate of energy transfer is power, denoted by P, so we write:

3. P = IV = I(IR) = I2R P = IV = (V/R)V = V2/R
Power relationships
P = IV = I(IR) = I2R
P = IV = (V/R)V = V2/R
Though these relationships are based on Ohm’s Law, they were first published in 1841 by James Joule.

4. Power
The upper rectangle represents a source with emf and internal resistance r, connected by ideal wires to an external circuit represented by the lower box.
Point a is at higher potential than point b, so Va > Vb and Vab is positive.
P = VabI

5. Bulbs in Series
Question: How does the brightness of bulb A compare with that of bulbs B and C?
Answer: Bulb A is brighter than bulb B and bulb C, which are of equal brightness.
Reason: The potential drop across bulb A is E, while the potential drop across B and across C is E/2. Thus, voltage and not current determines the brightness.

6. Example: Lighting Up a Flashlight
A 6 W flashlight bulb is powered by a 3 V battery having an internal resistance of 1 W. (Assume ideal wires.)
What is the power dissipation of the bulb?
What is the terminal voltage of the battery?
Note that in this situation, 14% of the available energy goes into heating the battery rather than providing light from the bulb.

7. Example: A Short-Circuited Car Battery
What is the short-circuit current of a 12 V car battery with an internal resistance of W?
What happens to the power supplied by the battery when it is shorted?
0.02 W
12 V
All of this power would be dissipated internally in the battery, making it likely to explode. Therefore, do not short out your car’s battery!

8. So a 5 W resistor or a 1/4 W resistor?
You are building a circuit that requires a 220 W resistor – you have a choice between a standard ¼ W resistor and a ”power” 5 W resistor. They have the same resistance, so which do you choose?
You choose the one that can handle up to twice the expected power dissipation of your resistor. For instance, an LED draws 15 mA of current and requires 5 V of potential to light – it will therefore dissipate ⨉ 5 = W while running, so if you need a resistor to knock down the voltage through the LED, you’re safe using a ¼ W resistor. There’s no problem with using power resistors all the time, expect that they are significantly larger than standard resistors.

9. Bulbs in Parallel
Initially, bulbs A and B have the same brightness and C is dark. What happens to the brightness of the bulbs when the switch is closed?
Bulb A gets brighter (because its potential change increases);
Bulb B gets dimmer (because current is diverted to Bulb C);
Bulb C glows with the same brightness as B (because they have the same voltage drop).

10. Power distribution systems
The figure below shows the basic idea of house wiring.
The “hot line” has an alternating sinusoidal voltage with a root-mean-square value of 120 V.
The “neutral line” is connected to “ground,” which is usually an electrode driven into the earth.

11. Grounding and GFI
Modern power wiring includes a “ground” line, the round 3rd wire of an electrical plug. The ground point defines a point of zero potential, which is normally connected directly to the Earth (Vearth=0). The operation of any circuit depends only on potential differences, so it should not be affected by the presence or absence of a ground connection.
Because the ground connection is connected at only one point, no current should flow through the ground connection. However, if some other part of a circuit is accidentally grounded, current is likely to flow through the ground line.
GFI (ground fault interruption) circuits, widely used, e.g., in bathroom wiring, detect current flow in the ground line and interrupt power automatically when it occurs. This has prevented many accidental electrocutions.

12. Circuit overloads
A fuse (Figure a) contains a link of lead–tin alloy with a very low melting temperature; the link melts and breaks the circuit when its rated current is exceeded.
A circuit breaker (Figure b) is an electromechanical device that performs the same function, using an electromagnet or a bimetallic strip to “trip” the breaker and interrupt the circuit when the current exceeds a specified value.
Circuit breakers have the advantage that they can be reset after they are tripped, while a blown fuse must be replaced.

13. Why it is safer to use a three-prong plug