Physics - Term 4 - Week 2

An electric circuit is a closed loop that allows current to flow. The basic components of a circuit include a power source (like a battery), conductors (wires), and loads (like resistors or bulbs). Understanding how these components interact is crucial for analyzing circuit behavior. Ohm's Law, which states that voltage (V) equals current (I) times resistance (R), is fundamental in this analysis.

Ohm's Law is a key principle in electronics and electrical engineering. It can be expressed mathematically as V = I × R. This relationship allows us to calculate the current flowing through a circuit if we know the voltage and resistance. For example, if a circuit has a voltage of 12 volts and a resistance of 4 ohms, the current can be calculated as I = V/R = 12V/4Ω = 3A.

In a series circuit, components are connected end-to-end, so the same current flows through each component. The total resistance in a series circuit is the sum of the individual resistances. In contrast, in a parallel circuit, components are connected across the same voltage source, and the total resistance can be calculated using the formula 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. Understanding these configurations is essential for circuit design and analysis.

Consider a series circuit with three resistors: R1 = 2Ω, R2 = 3Ω, and R3 = 5Ω. To find the total resistance, we add the resistances: R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω. If the circuit is powered by a 20V battery, we can find the current using Ohm's Law: I = V/R_total = 20V/10Ω = 2A.

In a parallel circuit with two resistors, R1 = 6Ω and R2 = 3Ω, we can calculate the total resistance using the formula: 1/R_total = 1/R1 + 1/R2. Thus, 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, which gives R_total = 2Ω. If the voltage across the circuit is 12V, the total current can be calculated as I_total = V/R_total = 12V/2Ω = 6A.

Let's work through a series circuit problem together. Suppose we have two resistors, R1 = 4Ω and R2 = 6Ω, connected in series with a 24V battery. First, calculate the total resistance: R_total = R1 + R2 = 4Ω + 6Ω = 10Ω. Now, apply Ohm's Law to find the current: I = V/R_total = 24V/10Ω = 2.4A. Discuss how the current would change if we added another resistor in series.

Now, let’s analyze a parallel circuit. We have two resistors, R1 = 12Ω and R2 = 4Ω, connected in parallel. Calculate the total resistance using the formula: 1/R_total = 1/R1 + 1/R2. This gives us 1/R_total = 1/12 + 1/4 = 1/12 + 3/12 = 4/12, so R_total = 3Ω. If the voltage across the circuit is 18V, what is the total current? Use I_total = V/R_total to find the answer.

Now it's your turn to practice. Solve the following problems: 1) A series circuit has resistors of 5Ω, 10Ω, and 15Ω. What is the total resistance? 2) A parallel circuit has resistors of 8Ω and 2Ω. Calculate the total resistance. 3) If a circuit with a total resistance of 4Ω is connected to a 16V battery, what is the current? Show your calculations.

• V = I + R
• V = I × R
• V = I / R
• V = R / I

Answer: V = I × R

Ohm's Law states that voltage equals current multiplied by resistance.

• R_total = R1 + R2 + R3
• R_total = 1/R1 + 1/R2 + 1/R3
• R_total = R1 × R2 × R3
• R_total = R1 - R2 - R3

Answer: R_total = R1 + R2 + R3

In a series circuit, the total resistance is the sum of the individual resistances.

• It increases
• It decreases
• It remains the same
• It doubles

Answer: It decreases

Adding more resistors in parallel decreases the total resistance.

Answer: 15Ω

Total resistance in series is the sum: 3Ω + 5Ω + 7Ω = 15Ω.

Answer: 5A

Using Ohm's Law: I = V/R = 10V/2Ω = 5A.

• 3Ω
• 4Ω
• 8Ω
• 16Ω

Answer: 3Ω

Using the formula: 1/R_total = 1/4 + 1/12 = 1/3, so R_total = 3Ω.

Answer: In series circuits, current is the same through all components, and total resistance is the sum of resistances. In parallel circuits, voltage is the same across all components, and total resistance is less than the smallest resistor.

This distinction affects how circuits behave under different loads.