Before electric power is defined, the formula is given to calculate it. The following formula can be used for any component in electric or electronic circuits:
in which P is the power consumed or generated by the component, V is the voltage across the component, and I is the current through the component. Again, this formula always works. But what does it mean? And how should the result be interpreted? In order to answer these questions, let’s start with a dimensional analysis.
The unit of power
The unit of voltage is volt (V), and since voltage is energy per unit of charge, 1 volt corresponds to 1 joule (J) per coulomb (C). The unit of current is ampere (A), and 1 ampere corresponds to 1 coulomb (C) per second (s). So the unit of power is (the brackets mean “the unit of…”):
The unit of power is watt (W). 1 watt corresponds to 1 joule per second. Power indicates how fast energy is consumed (or generated).
Power versus energy
For many students it takes a while before they grasp the concepts of power and energy, and the relation between them. Here is an analogy that might help. The amount of fuel (typically expressed in liters or gallons) in your car corresponds with an equivalent amount of energy (expressed in joule). The more fuel you have, the more energy you have at your disposal. Amount of fuel and amount of energy are linearly related. The amount of fuel and thus the amount of energy also determines how far you can go with your car.
Once you start riding your car, you will consume fuel. The rate at which this happens corresponds to power. Your fuel consumption (typically expressed in liters/100 km or gallons/100 km) is linearly related with power (expressed in joule per second or watt). If you accelerate fast or drive uphill, more power is involved than accelerating slowly or driving downhill.
The relation between power and energy is given in this formula, assuming the power P is constant:
in which ΔE is the energy consumption during time interval Δt. So, the longer a certain power consumption is maintained, the more energy is needed. In car language, the farther you want to ride, the more fuel you need. Power can thus be defined as the rate at which energy is consumed (or generated):
Power in a resistor
Basics - Level 3
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A few simple questions to practice.
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Question 1 of 5
Again, the first question is a simple calculation. What is the voltage across a resistor if the current is 15 mA and the power is 45 mW?Correct
Indeed, 45 mW divided by 15 mA is 3V.Incorrect
Since P = V.I, then V = P / I.
The formula for power is P = V.I. The m before the unit means 10-3.
Question 2 of 5
Resistors R1 and R2 have the same current during 10 seconds. The voltage across R1 is four times larger. Which of the following statements is incorrect?Correct
Indeed, a tricky one because the statement would still be correct under the assumption that the current would remain the same. However, it is not known whether this assumption is true, so we can not generalize this statement.Incorrect
In order to have the same power consumption in both resistors, resistor R2 should be four times larger AND still have the same current. However, we do not know whether the latter is true, so this statement cannot be generalized.
You need two formula’s: Ohm’s Law and the formula for power.
Question 3 of 5
Consider the special case of a resistor with zero resistance (R = 0 Ω). What can you say about the power consumption in this resistor?Correct
Indeed. For any current, the voltage will be zero according to Ohm’s Law. Since P = V.I, P will be 0 W.Incorrect
For any current, the voltage will be zero according to Ohm’s Law. Since P = V.I, P will be 0 W.
Use Ohm’s Law first to derive a conclusion on the voltage.
Question 4 of 5
Suppose the voltage across a given resistor is doubled. What happens with the power?Correct
Great job! Indeed, the voltage doubles AND the current doubles, leading to a factor of 4.Incorrect
Since the voltage doubles, the current also doubles, leading to a factor of 4.
Again, combine Ohm’s Law with the formula for power.
Question 5 of 5
Now consider the special case of an infinitely high resistance (R = ∞Ω). Which of the following statements is incorrect?Correct
Indeed, this statement is false, so your answer is correct.Incorrect
You indeed do not know the voltage, but that does not mean it is infinity.