Technical Science - Term 3 - Week 7

Ohm's Law is a fundamental principle in electrical engineering that states the relationship between voltage (V), current (I), and resistance (R) in a circuit. It can be expressed with the formula V = I × R. This means that the voltage across a conductor is directly proportional to the current flowing through it, provided the temperature remains constant. Understanding this law is crucial for analyzing and designing electrical circuits.

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 (R_total = R1 + R2 + ... + Rn). In contrast, parallel circuits have components connected across the same voltage source, allowing multiple paths for current. The total resistance in a parallel circuit can be calculated 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 of 12 volts and a resistance of 4 ohms. To find the current, we can rearrange Ohm's Law: I = V/R. Substituting the values, we get I = 12V / 4Ω = 3A. This means that a current of 3 amperes flows through the circuit.

Suppose we have three resistors in series: R1 = 2Ω, R2 = 3Ω, and R3 = 5Ω. To find the total resistance, we add them together: R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω. Therefore, the total resistance of the series circuit is 10 ohms.

Let's work through a problem together. If we have a circuit with a voltage of 24 volts and a resistance of 6 ohms, what is the current? Start by applying Ohm's Law: I = V/R. Substitute the values: I = 24V / 6Ω. Calculate the current and share your answer with the class.

Now, let's find the total resistance of two resistors in parallel: R1 = 4Ω and R2 = 12Ω. Use the formula 1/R_total = 1/R1 + 1/R2. Substitute the values: 1/R_total = 1/4 + 1/12. Calculate the total resistance and discuss your findings with a partner.

For independent practice, solve the following problems: 1) A circuit has a voltage of 30 volts and a resistance of 10 ohms. Calculate the current. 2) Find the total resistance of three resistors in series: R1 = 5Ω, R2 = 10Ω, R3 = 15Ω. 3) Calculate the total resistance of two resistors in parallel: R1 = 6Ω and R2 = 3Ω. Show your work and be prepared to discuss your solutions in class.

• 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).

• It splits equally
• It varies with each component
• It remains the same
• It increases with each component

Answer: It remains the same

In a series circuit, the same current flows through all components.

• 3Ω
• 4Ω
• 8Ω
• 16Ω

Answer: 3Ω

Using the formula 1/R_total = 1/R1 + 1/R2, we find R_total = 3Ω.

Answer: 4A

Using Ohm's Law, I = V/R = 48V / 12Ω = 4A.

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

Answer: It increases

Adding more resistors in series increases the total resistance.

Answer: 10Ω

The total resistance is R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω.

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

Answer: Voltage is the same across all components

In parallel circuits, the voltage across each component is the same.