Technical Science - Term 3 - Week 10

An electrical circuit is a closed loop that allows electric current to flow. It consists of various components such as resistors, capacitors, and power sources. Understanding how these components interact is crucial for analyzing and designing circuits. The flow of current is driven by voltage, and the relationship between voltage, current, and resistance is defined by Ohm's Law, which states that V = I × R, where V is voltage, I is current, and R is resistance.

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, a parallel circuit has components connected across the same voltage source, allowing multiple paths for current to flow. The total resistance in a parallel circuit is found using the formula 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. Understanding these configurations is essential for circuit design and troubleshooting.

Consider a circuit with a voltage supply of 12 volts and a resistor of 4 ohms. To find the current flowing through the circuit, we apply Ohm's Law: I = V/R. Substituting the values, we get I = 12V / 4Ω = 3A. This means that 3 amperes of current flow through the circuit. This example illustrates how to use Ohm's Law to determine current in a simple circuit.

Suppose we have three resistors in series: R1 = 2Ω, R2 = 3Ω, and R3 = 5Ω. The total resistance (R_total) can be calculated as R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω. This total resistance affects the overall current in the circuit when connected to a voltage source.

Let's work through a problem together. We have a parallel circuit with two resistors: R1 = 6Ω and R2 = 3Ω connected to a 12V battery. First, we calculate the total resistance using the formula 1/R_total = 1/R1 + 1/R2. Substituting the values gives us 1/R_total = 1/6 + 1/3. Simplifying this, we find R_total = 2Ω. Now, using Ohm's Law, we can find the total current: I_total = V/R_total = 12V / 2Ω = 6A. This shows how to analyze a parallel circuit step-by-step.

Now it's your turn! Solve the following problems independently: 1) A series circuit has a 9V battery and two resistors, R1 = 1Ω and R2 = 2Ω. Calculate the total current flowing through the circuit. 2) In a parallel circuit with R1 = 4Ω and R2 = 8Ω connected to a 24V battery, find the total current. Show all your calculations and reasoning.

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

Answer: V = I × R

Ohm's Law states that voltage (V) is equal to the current (I) multiplied by the resistance (R).

• The sum of individual resistances
• The product of individual resistances
• The average of individual resistances
• Always equal to the smallest resistance

Answer: The sum of individual resistances

In a series circuit, the total resistance is calculated by adding all individual resistances together.

Answer: A parallel circuit is a type of electrical circuit where components are connected across the same voltage source, allowing multiple paths for current to flow.

This definition highlights the key characteristic of parallel circuits, which is the ability to have multiple pathways for current.

• It decreases
• It increases
• It remains the same
• It becomes zero

Answer: It increases

Adding more resistors in parallel provides additional paths for current, thus increasing the total current.

Answer: Total resistance R_total = 3Ω.

Using the formula 1/R_total = 1/R1 + 1/R2 gives 1/R_total = 1/4 + 1/12, leading to R_total = 3Ω.

• 4A
• 6A
• 8A
• 12A

Answer: 4A

Using Ohm's Law, I = V/R = 24V / 6Ω = 4A.

• Resistor