Technical Science - Term 4 - Week 9

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 (like resistors or light bulbs). Understanding how these components interact is crucial for analyzing and designing circuits.

Ohm's Law is a fundamental principle in electronics 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 law helps us calculate how much current will flow in a circuit for a given voltage and resistance, which is essential for circuit design and troubleshooting.

In a series circuit, components are connected end-to-end, so the same current flows through all components. 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, which affects how devices operate within the circuit.

Consider a circuit with a voltage of 12 volts and a resistance of 4 ohms. To find the current, we apply 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.

If 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. Therefore, R_total = 2Ω + 3Ω + 5Ω = 10Ω. This total resistance affects the current flow in the circuit.

For resistors in parallel, the formula is 1/R_total = 1/R1 + 1/R2 + 1/R3. If R1 = 6Ω, R2 = 3Ω, and R3 = 2Ω, we calculate: 1/R_total = 1/6 + 1/3 + 1/2. Finding a common denominator (6), we get 1/R_total = 1/6 + 2/6 + 3/6 = 6/6. Thus, R_total = 1Ω.

Let's work through a problem together. A circuit has a voltage of 24 volts and a resistance of 8 ohms. What is the current? Using Ohm's Law, we apply I = V / R. Substituting the values, we find I = 24V / 8Ω = 3A. Now, try calculating the current for a circuit with 30 volts and 10 ohms.

Now, let's calculate the total resistance of a series circuit with resistors of 4Ω, 5Ω, and 6Ω. We add them together: R_total = 4Ω + 5Ω + 6Ω = 15Ω. Discuss with your partner how this total resistance would affect the current if the voltage is 30 volts.

For a parallel circuit with resistors of 12Ω, 4Ω, and 3Ω, let's calculate the total resistance. Using the formula 1/R_total = 1/R1 + 1/R2 + 1/R3, we find: 1/R_total = 1/12 + 1/4 + 1/3. Calculate the total resistance and discuss how it differs from a series circuit.

Complete the following problems on your own: 1) A circuit has a voltage of 48 volts and a resistance of 12 ohms. Calculate the current. 2) If the current in a circuit is 5A and the resistance is 10Ω, what is the voltage? Show your calculations.

You have three resistors: R1 = 10Ω, R2 = 15Ω, and R3 = 20Ω connected in series. Calculate the total resistance and discuss how this would affect the current if the circuit is powered by a 60V source.

Given three resistors in parallel: R1 = 8Ω, R2 = 4Ω, and R3 = 2Ω, calculate the total resistance. After calculating, explain how the total resistance in this parallel circuit compares to a series circuit with the same resistors.

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

Answer: V = I × R

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

• The sum of all resistances
• The average of all resistances
• The product of all resistances
• The smallest resistance

Answer: The sum of all resistances

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

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

Answer: It decreases

In a parallel circuit, the total resistance is always less than the smallest individual resistance.

Answer: 4A

Using Ohm's Law, I = V / R = 36V / 9Ω = 4A.

Answer: 10V

Using Ohm's Law, V = I × R = 2A × 5Ω = 10V.

• Current is the same through all components
• Voltage is the same across all components
• Resistance is the same across all components
• All components must be connected in a single path

Answer: Voltage is the same across all components

In a parallel circuit, all components share the same voltage from the power source.

Answer: 18Ω

The total resistance in a series circuit is the sum: 3Ω + 6Ω + 9Ω = 18Ω.