Potential difference & Power
This lesson covers:
- Defining potential difference (voltage) as work done per unit charge.
- Relating potential difference to the kinetic energy gained by a charged particle.
- Defining power as the rate of energy transfer
- Calculating power in electrical circuits using P=VI
- Using V=IR to derive other power equations
Potential difference is work done per unit charge
Potential difference (V) is the work done (W) per unit charge (Q):
V=QW
Where:
V = potential difference (V)
W = work done (J)
Q = Charge (C)
A potential difference of one volt means one joule of work is transferred for each coulomb of charge moving through it:
1 V=1 C1 J
Worked example - Calculating potential difference
Calculate the potential difference across a component if 50 joules of work is done to move a charge of 10 coulombs.
Step 1: Formula
V = QW
Step 2: Substitution and correct evaluation
V = 1050=5 V
Relating potential difference to kinetic energy
When a charge is accelerated due to a potential difference, it gains kinetic energy. For an electron with a charge of -e, the work done (W) can be equated to its kinetic energy:
W = V e = 21 m v2
Where:
W = work done (J)
V = potential difference (V)
e = charge of an electron (1.6 ×10−19 C)
m = mass of electron (9.11×10−31 kg)
v = velocity (m s−1)
Worked example - Kinetic energy of an electron
Calculate the speed of an electron accelerated through a potential difference of 12 volts.
Step 1: Formula
W = V e = 21m v2
Step 2: Calculate Work Done (W)
W = V × e
W = 12×−1.6×10−19=−1.92×10−18 J
Step 3: Calculate electron speed
v = √m2×W
v = √9.11×10−312×−1.92×10−18=2.05×106 m s−1
Power is the rate of energy transfer
Power (P) measures the rate of energy transfer or rate of doing work:
P = tW
Where:
P = power (W)
W = Work done (J)
t = time (s)
Power has a simple formula for electrical circuits:
P = V I
Where:
P = power (W)
V = potential difference (V)
I = current (A)
Other power equations
We know V=IR from the definition of resistance R. Substituting this into P=VI gives:
P = RV2
P = I2 R
The choice of equation depends on the quantities provided.
Electrical energy
Work done (W) is power multiplied by time:
W = P t = V I t
Where:
W = energy transferred (W)
P = Power (W)
t = times (s)
V = potential difference (V)
I = current (A)
Worked example - Calculating energy transfer
An electric kettle draws a current of 4A when connected to the 230V mains supply. It takes 270 seconds to boil the water.
Calculate the electrical energy transferred.
Step 1: Formula
W = V I t
Step 2: Substitution and correct evaluation
W = 230×4×270=248,400 J