Technical Science - Term 4 - Week 6

An electrical circuit is a closed loop that allows current to flow from a power source through various components and back to the source. The basic components of a circuit include a power source (like a battery), conductors (wires), and loads (devices that use electricity). Understanding how these components interact is crucial for analyzing and designing circuits.

Ohm's Law is a fundamental principle in electronics that relates voltage (V), current (I), and resistance (R) in a circuit. It states that V = I × R. This relationship allows us to calculate one of these values if the other two are known. 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 is the sum of individual resistances. In contrast, a parallel circuit has components connected across the same voltage source, allowing multiple paths for current. The total resistance in a parallel circuit is less than the smallest individual resistance, calculated using the formula 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn.

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.

If we have three resistors in series with values of 2Ω, 3Ω, and 5Ω, the total resistance can be calculated as R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω. This total resistance affects the current flowing through the circuit.

For two resistors in parallel, one with 4Ω and the other with 6Ω, we calculate the total resistance using the formula: 1/R_total = 1/R1 + 1/R2 = 1/4 + 1/6. Finding a common denominator (12), we have 1/R_total = 3/12 + 2/12 = 5/12, thus R_total = 12/5 = 2.4Ω.

Let's work together on a problem. A circuit has a voltage of 30 volts and a resistance of 10 ohms. Using Ohm's Law, calculate the current. Students should apply the formula I = V/R. The expected answer is I = 30V/10Ω = 3A.

Look at the following circuit diagram. Identify whether the resistors are in series or parallel. Discuss with your partner the characteristics that led you to your conclusion. Remember, in series, the current is the same, while in parallel, the voltage is the same across all components.

Calculate the total resistance for a series circuit with resistors of 5Ω, 10Ω, and 15Ω. Students should add the resistances together: R_total = 5Ω + 10Ω + 15Ω = 30Ω. Discuss how this affects the current in the circuit.

Individually, calculate the current for a circuit with a voltage of 50 volts and a resistance of 25 ohms. Use Ohm's Law to find the answer and be prepared to explain your reasoning.

Create a series circuit diagram with three resistors of your choice. Calculate the total resistance and the current if the voltage supply is 12 volts. Present your findings to the class.

Design a parallel circuit with two resistors, one of 8Ω and another of 4Ω. Calculate the total resistance and the current if the voltage supply is 24 volts. Write a short explanation of how the current divides in the circuit.

• V = I × R
• R = V/I
• I = V/R
• All of the above

Answer: All of the above

All three formulas are derived from Ohm's Law and can be used depending on which variables are known.

• Less than the smallest resistor
• Equal to the sum of all resistors
• The same as the voltage
• None of the above

Answer: Equal to the sum of all resistors

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

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

Answer: It increases

Adding more branches in a parallel circuit provides additional paths for current, thus increasing the total current.

Answer: 4A

Using Ohm's Law, I = V/R = 60V/15Ω = 4A.

Answer: 6.67Ω

Using the formula 1/R_total = 1/R1 + 1/R2, we find R_total = 1/(1/10 + 1/20) = 6.67Ω.

• Voltage is the same across all components
• Current is the same through all components
• Resistance is the same for all components
• Power is the same for all components

Answer: Current is the same through all components

In a series circuit, the same current flows through each component.

• It doubles