Technical Science - Term 3 - Week 5

An electrical circuit is a closed loop that allows current to flow. It consists of various components such as resistors, capacitors, and power sources. Understanding how these components interact is crucial for analyzing circuit behavior. The basic principle governing electrical circuits is Ohm's Law, which states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor.

Ohm's Law is expressed with the formula V = I × R. This means that if you know any two of the three variables (voltage, current, resistance), you can calculate the third. 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. This law is fundamental in designing and analyzing circuits.

In a series circuit, components are connected end-to-end, so the same current flows through all components. The total resistance in a series circuit is the sum of the individual resistances (R_total = R1 + R2 + ... + Rn). 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.

Consider a circuit with a voltage of 24 volts and a resistance of 6 ohms. To find the current, we apply Ohm's Law: I = V/R = 24V/6Ω = 4A. This means that 4 amperes of current flow through the circuit. This example illustrates how to manipulate the formula to find the desired variable.

Suppose we have three resistors in series: R1 = 2Ω, R2 = 3Ω, and R3 = 5Ω. The total resistance is calculated as R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω. This total resistance affects the current flowing through the circuit when a voltage is applied.

For resistors in parallel, let’s say R1 = 4Ω and R2 = 4Ω. The total resistance can be calculated using the formula 1/R_total = 1/R1 + 1/R2. Thus, 1/R_total = 1/4 + 1/4 = 1/2, which gives R_total = 2Ω. This lower total resistance allows more current to flow compared to a series configuration.

Let's work through a problem together. A circuit has a voltage of 30 volts and a resistance of 10 ohms. What is the current? Using Ohm's Law, we find I = V/R = 30V/10Ω = 3A. Now, try to solve a similar problem with a voltage of 50 volts and a resistance of 25 ohms. What is the current?

In groups, identify whether the following circuits are series or parallel: Circuit A has three light bulbs connected in a single path, while Circuit B has three light bulbs connected across the same two points. Discuss how the configuration affects the brightness of the bulbs and the total resistance.

Let’s calculate the total resistance of a series circuit with resistors of 5Ω, 10Ω, and 15Ω. What is the total resistance? R_total = 5Ω + 10Ω + 15Ω = 30Ω. Now, calculate the total resistance for two resistors in parallel, 6Ω and 3Ω. What do you find?

Complete the following problems independently: 1) A circuit has a voltage of 12 volts and a resistance of 3 ohms. Calculate the current. 2) If the current in a circuit is 2A and the resistance is 4Ω, what is the voltage? Show your calculations.

Solve the following: 1) Find the total resistance of a series circuit with resistors of 8Ω, 4Ω, and 2Ω. 2) Calculate the total resistance of two resistors in parallel, 12Ω and 6Ω. Write down your answers and the steps you took to arrive at them.

Design a simple circuit using two resistors of your choice. Calculate the total resistance and the current if the circuit is powered by a 9V battery. Present your findings to the class, explaining your calculations.

• Voltage, current, and power
• Voltage, current, and resistance
• Current, resistance, and capacitance
• Voltage, capacitance, and power

Answer: Voltage, current, and resistance

Ohm's Law states that voltage is equal to the current multiplied by resistance.

• 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.

• 3A
• 2A
• 1A
• 4A

Answer: 3A

Using Ohm's Law, I = V/R = 24V/8Ω = 3A.

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

In a parallel circuit, each component receives the same voltage, and the total current is the sum of the currents through each component.

Answer: 15Ω

In a series circuit, total resistance is the sum: R_total = R1 + R2 = 5Ω + 10Ω = 15Ω.

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

Answer: It decreases

Adding more resistors in parallel decreases the total resistance because there are more paths for current to flow.