IB MYP 4-5 Physics- Series and parallel circuits- Study Notes - New Syllabus
IB MYP 4-5 Physics-Series and parallel circuits- Study Notes
Key Concepts
- Series and parallel circuits
Series and Parallel Circuits
Series and Parallel Circuits
Series Circuits
In a series circuit, components are connected end-to-end, so the current flows through one path only.
Current: The same current flows through all components.
\( I = I_1 = I_2 = I_3 \,… \)
Voltage: The total potential difference is shared across components.
\( V = V_1 + V_2 + V_3 \,… \)
Resistance: The total resistance is the sum of all resistances.
\( R = R_1 + R_2 + R_3 \,… \)
- If one component breaks, the whole circuit stops working.
- Example: Old Christmas lights (if one bulb blows, all go out).
Parallel Circuits
In a parallel circuit, components are connected across multiple branches, so the current has more than one path to flow.
Current: The total current is divided among the branches.
\( I = I_1 + I_2 + I_3 \,… \)
Current in Parallel Circuits (Two Resistors)
When resistors are connected in parallel, the voltage across each branch is the same, but the current is divided between the branches depending on the resistance values.
Ohm’s law: \( I = \dfrac{V}{R} \)
- The potential difference across each parallel branch is the same.
- The total current supplied by the source is the sum of the branch currents.
- Branch with smaller resistance carries larger current.
Total current: \( I_{total} = I_1 + I_2 \)
Where: \( I_1 = \dfrac{V}{R_1} \), \( I_2 = \dfrac{V}{R_2} \)
Voltage: The potential difference across each branch is the same.
\( V = V_1 = V_2 = V_3 \,… \)
Resistance: The reciprocal of total resistance is the sum of reciprocals of branch resistances.
\( \dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} \,… \)
- If one branch breaks, current can still flow through other branches.
- Example: Household wiring (appliances work independently).
Comparison:
| Feature | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same through all components | Divided among branches |
| Voltage | Shared among components | Same across each branch |
| Resistance | Adds up: \( R = R_1 + R_2 \,… \) | \( \dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} \,… \) |
| Effect of Break | Whole circuit stops | Other branches still work |
| Example | Fairy lights in series | House wiring |
Example:
Two resistors of \( 4 \, \Omega \) and \( 6 \, \Omega \) are connected in series with a 12 V battery. Find the total resistance, current, and voltage across each resistor.
▶️ Answer/Explanation
Total resistance: \( R = 4 + 6 = 10 \, \Omega \).
Current: \( I = \dfrac{V}{R} = \dfrac{12}{10} = 1.2 \, A \).
Voltage across \( R_1 = IR_1 = 1.2 \times 4 = 4.8 \, V \).
Voltage across \( R_2 = IR_2 = 1.2 \times 6 = 7.2 \, V \).
Final Answer: \( \boxed{R = 10 \, \Omega, \, I = 1.2 \, A, \, V_1 = 4.8 \, V, \, V_2 = 7.2 \, V} \).
Example:
Two resistors of \( 6 \, \Omega \) and \( 3 \, \Omega \) are connected in parallel across a 12 V battery. Find the total resistance and current in each branch.
▶️ Answer/Explanation
Reciprocal resistance: \( \dfrac{1}{R} = \dfrac{1}{6} + \dfrac{1}{3} = \dfrac{1}{6} + \dfrac{2}{6} = \dfrac{3}{6} \).
So \( R = 2 \, \Omega \).
Total current: \( I = \dfrac{V}{R} = \dfrac{12}{2} = 6 \, A \).
Current in 6 Ω branch: \( I_1 = \dfrac{V}{R_1} = \dfrac{12}{6} = 2 \, A \).
Current in 3 Ω branch: \( I_2 = \dfrac{V}{R_2} = \dfrac{12}{3} = 4 \, A \).
Final Answer: \( \boxed{R = 2 \, \Omega, \, I = 6 \, A, \, I_1 = 2 \, A, \, I_2 = 4 \, A} \).
Example:
A 2 Ω resistor is in series with a parallel combination of two 4 Ω resistors. The circuit is connected to a 12 V battery. Find the total resistance.
▶️ Answer/Explanation
Parallel part: \( \dfrac{1}{R_p} = \dfrac{1}{4} + \dfrac{1}{4} = \dfrac{2}{4} = \dfrac{1}{2} \).
So \( R_p = 2 \, \Omega \).
Total resistance: \( R = 2 + 2 = 4 \, \Omega \).
Final Answer: \( \boxed{R = 4 \, \Omega} \).