IB Physics Topic B.5.4 Power and Resistor…

Electrical Power in Resistors

In electrical circuits, power is dissipated as thermal energy in resistors.
The formula for power in a resistor is:$$
P = IV
$$ where:
1. P is the power (in watts, W)
2. I is the current (in amperes, A)
3. V is the potential difference (in volts, V)
Using Ohm’s Law ($V = IR$), we can express power in two other forms:
In terms of current and resistance:$$
P = I^2R
$$
In terms of voltage and resistance:$$
P = \frac{V^2}{R}
$$

Tip

Choose the power formula that matches the information you have.
If you know the current and resistance, use $P = I^2R$.
If you know the voltage and resistance, use $P = \frac{V^2}{R}$.

Example question

A resistor has a resistance of 5 Ω and a current of 2 A flowing through it. Calculate the power dissipated.

Solution

Using $P = I^2R$:

$$
P = (2 \, \mathrm{A})^2 \times 5 \, \Omega = 20 \, \mathrm{W}
$$

Resistors in Series Circuits

Key Characteristics of Series Circuits

Current: The current is the same through all resistors. $$
I = I_1 = I_2 = I_3 = \ldots
$$
Voltage: The total voltage across the circuit is the sum of the voltages across each resistor. $$
V = V_1 + V_2 + V_3 + \ldots
$$
Resistance: The total resistance is the sum of the individual resistances. $$
R_s = R_1 + R_2 + R_3 + \ldots
$$

Tip

In series circuits, adding more resistors increases the total resistance, which decreases the current for a given voltage.

Example question

Three resistors with resistances 2 Ω, 4 Ω, and 6 Ω are connected in series. Calculate the total resistance and the current if the total voltage is 12 V.

Solution

Total Resistance:$$
R_s = 2 \, \Omega + 4 \, \Omega + 6 \, \Omega = 12 \, \Omega
$$
Current (using Ohm’s Law, $I = \frac{V}{R}$):$$
I = \frac{12 \, \mathrm{V}}{12 \, \Omega} = 1 \, \mathrm{A}
$$

Resistors in Parallel Circuits

Key Characteristics of Parallel Circuits

Voltage: The voltage across each resistor is the same. $$
V = V_1 = V_2 = V_3 = \ldots
$$
Current: The total current is the sum of the currents through each resistor. $$
I = I_1 + I_2 + I_3 + \ldots
$$
Resistance: The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. $$
\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots
$$

Tip

In parallel circuits, adding more resistors decreases the total resistance, which increases the current for a given voltage.

Example question

Three resistors with resistances 2 Ω, 4 Ω, and 6 Ω are connected in parallel. Calculate the total resistance and the current if the total voltage is 12 V.

Solution

Total Resistance:$$ \frac{1}{R_p} = \frac{1}{2} + \frac{1}{4} + \frac{1}{6} = \frac{6}{12} + \frac{3}{12} + \frac{2}{12} = \frac{11}{12}, \quad R_p = \frac{12}{11} \, \Omega \approx 1.09 \, \Omega $$
Total Current (using Ohm’s Law, $I = \frac{V}{R}$):$$
I = \frac{12 \, \mathrm{V}}{1.09 \, \Omega} \approx 11.01 \, \mathrm{A}
$$

Combining Series and Parallel Circuits

Many circuits contain a combination of series and parallel resistors.
To analyze these circuits:
1. Simplify the circuit by reducing series and parallel groups step-by-step.
2. Calculate the total resistance.
3. Use Ohm’s Law to find the total current.
4. Work backward to find the current, voltage, or power for individual resistors.

Common Mistake

A common mistake is to assume that current is the same in parallel resistors.
Remember, current splits in parallel paths, but voltage remains constant across each path.

Example question

Consider a circuit with three resistors: 2 Ω and 4 Ω in series, and a 6 Ω resistor in parallel with the series combination. The total voltage is 12 V. Calculate the current through each series resistor.

Solution

Simplify the Series Resistors:$$
R_s = 2\ \Omega + 4\ \Omega = 6\ \Omega
$$
Combine with the Parallel Resistor:$$ \frac{1}{R_{\mathrm{total}}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}, \quad R_{\mathrm{total}} = 3\ \Omega $$
Calculate the Total Current: $$
I = \frac{12\ \mathrm{V}}{3\ \Omega} = 4\ \mathrm{A}
$$
Find the Voltage Across the Series Resistors:$$ V_s = 12\ \mathrm{V} $$
Find the Current Through Each Series Resistor (same current in series):
- 2 Ω resistor: $I = 4\ \mathrm{A}$
- 4 Ω resistor: $I = 4\ \mathrm{A}$

Active recall

Write down the three equivalent expressions for the power dissipated in a resistor.
How does the total resistance change when resistors are added in series?
How does the total resistance change when resistors are added in parallel?
In a parallel circuit, which quantity is the same across each resistor?

Electrical Power in Resistors

In electrical circuits, power is dissipated as thermal energy in resistors.
The formula for power in a resistor is:$$
P = IV
$$ where:
1. P is the power (in watts, W)
2. I is the current (in amperes, A)
3. V is the potential difference (in volts, V)
Using Ohm’s Law ($V = IR$), we can express power in two other forms:
In terms of current and resistance:$$
P = I^2R
$$
In terms of voltage and resistance:$$
P = \frac{V^2}{R}
$$

Tip

Choose the power formula that matches the information you have.
If you know the current and resistance, use $P = I^2R$.
If you know the voltage and resistance, use $P = \frac{V^2}{R}$.

Example question

A resistor has a resistance of 5 Ω and a current of 2 A flowing through it. Calculate the power dissipated.

Solution

Using $P = I^2R$:

$$
P = (2 \, \mathrm{A})^2 \times 5 \, \Omega = 20 \, \mathrm{W}
$$

Resistors in Series Circuits

Key Characteristics of Series Circuits

Current: The current is the same through all resistors. $$
I = I_1 = I_2 = I_3 = \ldots
$$
Voltage: The total voltage across the circuit is the sum of the voltages across each resistor. $$
V = V_1 + V_2 + V_3 + \ldots
$$
Resistance: The total resistance is the sum of the individual resistances. $$
R_s = R_1 + R_2 + R_3 + \ldots
$$

Tip

In series circuits, adding more resistors increases the total resistance, which decreases the current for a given voltage.

Example question

Three resistors with resistances 2 Ω, 4 Ω, and 6 Ω are connected in series. Calculate the total resistance and the current if the total voltage is 12 V.

Solution

Total Resistance:$$
R_s = 2 \, \Omega + 4 \, \Omega + 6 \, \Omega = 12 \, \Omega
$$
Current (using Ohm’s Law, $I = \frac{V}{R}$):$$
I = \frac{12 \, \mathrm{V}}{12 \, \Omega} = 1 \, \mathrm{A}
$$

Resistors in Parallel Circuits

Key Characteristics of Parallel Circuits

Voltage: The voltage across each resistor is the same. $$
V = V_1 = V_2 = V_3 = \ldots
$$
Current: The total current is the sum of the currents through each resistor. $$
I = I_1 + I_2 + I_3 + \ldots
$$
Resistance: The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. $$
\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots
$$

Tip

In parallel circuits, adding more resistors decreases the total resistance, which increases the current for a given voltage.

Example question

Three resistors with resistances 2 Ω, 4 Ω, and 6 Ω are connected in parallel. Calculate the total resistance and the current if the total voltage is 12 V.

Solution

Total Resistance:$$ \frac{1}{R_p} = \frac{1}{2} + \frac{1}{4} + \frac{1}{6} = \frac{6}{12} + \frac{3}{12} + \frac{2}{12} = \frac{11}{12}, \quad R_p = \frac{12}{11} \, \Omega \approx 1.09 \, \Omega $$
Total Current (using Ohm’s Law, $I = \frac{V}{R}$):$$
I = \frac{12 \, \mathrm{V}}{1.09 \, \Omega} \approx 11.01 \, \mathrm{A}
$$

Combining Series and Parallel Circuits

Many circuits contain a combination of series and parallel resistors.
To analyze these circuits:
1. Simplify the circuit by reducing series and parallel groups step-by-step.
2. Calculate the total resistance.
3. Use Ohm’s Law to find the total current.
4. Work backward to find the current, voltage, or power for individual resistors.

Common Mistake

A common mistake is to assume that current is the same in parallel resistors.
Remember, current splits in parallel paths, but voltage remains constant across each path.

Example question

Solution

Simplify the Series Resistors:$$
R_s = 2\ \Omega + 4\ \Omega = 6\ \Omega
$$
Combine with the Parallel Resistor:$$ \frac{1}{R_{\mathrm{total}}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}, \quad R_{\mathrm{total}} = 3\ \Omega $$
Calculate the Total Current: $$
I = \frac{12\ \mathrm{V}}{3\ \Omega} = 4\ \mathrm{A}
$$
Find the Voltage Across the Series Resistors:$$ V_s = 12\ \mathrm{V} $$
Find the Current Through Each Series Resistor (same current in series):
- 2 Ω resistor: $I = 4\ \mathrm{A}$
- 4 Ω resistor: $I = 4\ \mathrm{A}$

Active recall

Write down the three equivalent expressions for the power dissipated in a resistor.
How does the total resistance change when resistors are added in series?
How does the total resistance change when resistors are added in parallel?
In a parallel circuit, which quantity is the same across each resistor?

IB Physics B.5.4 Power and Resistor Configurations Notes

IB Physics B.5.4 Power and Resistor Configurations Notes

Electrical Power in Resistors

Resistors in Series Circuits

Key Characteristics of Series Circuits

Resistors in Parallel Circuits

Key Characteristics of Parallel Circuits

Combining Series and Parallel Circuits

Electrical Power in Resistors

Resistors in Series Circuits

Key Characteristics of Series Circuits

Resistors in Parallel Circuits

Key Characteristics of Parallel Circuits

Combining Series and Parallel Circuits

IB Physics B.5.4 Power and Resistor Configurations Notes

Topic A - Space, time and motion

Topic B - The particulate nature of matter

Topic C - Wave behaviour

Topic D - Fields

Topic E - Nuclear and quantum physics

IB Physics B.5.4 Power and Resistor Configurations Notes

Topic A - Space, time and motion

Topic B - The particulate nature of matter

Topic C - Wave behaviour

Topic D - Fields

Topic E - Nuclear and quantum physics

Electrical Power in Resistors

Resistors in Series Circuits

Key Characteristics of Series Circuits

Resistors in Parallel Circuits

Key Characteristics of Parallel Circuits

Combining Series and Parallel Circuits

Electrical Power in Resistors

Resistors in Series Circuits

Key Characteristics of Series Circuits

Resistors in Parallel Circuits

Key Characteristics of Parallel Circuits

Combining Series and Parallel Circuits