Technical Science - Term 3 - Week 2

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 states that the current (I) 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. This relationship can be expressed with the formula: V = I × R. This law is fundamental in calculating how much current will flow in a circuit given a certain voltage and resistance.

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. 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 can be calculated using the formula: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn.

If a circuit has a voltage of 12 volts and a resistance of 4 ohms, we can find the current using Ohm's Law. Rearranging the formula gives us I = V/R. Substituting the values, we get I = 12V / 4Ω = 3A. Therefore, the current flowing through the circuit is 3 amperes.

Consider a series circuit with three resistors: R1 = 2Ω, R2 = 3Ω, and R3 = 5Ω. The total resistance (R_total) is calculated as R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω. Thus, the total resistance in the series circuit is 10 ohms.

For a parallel circuit with two resistors: R1 = 6Ω and R2 = 3Ω, we can find the total resistance using the formula 1/R_total = 1/R1 + 1/R2. This gives us 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Therefore, R_total = 6/3 = 2Ω. The total resistance in this parallel circuit is 2 ohms.

Let's work through a problem together. If we have a circuit with 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 in a series circuit with resistors of 4Ω, 6Ω, and 10Ω. Adding these together, we find R_total = 4Ω + 6Ω + 10Ω = 20Ω. Discuss with your partner how the current would change if one of the resistors was removed from the circuit.

Consider a parallel circuit with three resistors: R1 = 12Ω, R2 = 4Ω, and R3 = 6Ω. To find the total resistance, we use the formula 1/R_total = 1/R1 + 1/R2 + 1/R3. Calculate this step by step and share your results with the class.

Complete the following problems on your own: 1) Calculate the current in a circuit with a voltage of 48 volts and a resistance of 12 ohms. 2) Find the total resistance in a series circuit with resistors of 5Ω, 15Ω, and 10Ω. 3) Determine the total resistance in a parallel circuit with resistors of 8Ω and 4Ω. Show all your calculations.

For those who finish early, try these challenge problems: 1) If a circuit has a total resistance of 10Ω and a current of 2A, what is the voltage? 2) In a parallel circuit with three resistors of 2Ω, 3Ω, and 6Ω, calculate the total resistance. Be prepared to explain your reasoning.

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

Answer: V = I × R

Ohm's Law states that voltage equals current multiplied by resistance.

• Always less than the smallest resistor
• The sum of all resistances
• The product of all resistances
• Equal to the largest resistor

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 stays the same
• It doubles

Answer: It decreases

Adding more resistors in parallel provides additional paths for current, which reduces the total resistance.

Answer: 4A

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

Answer: 15Ω

Total resistance in series is R_total = R1 + R2 + R3 = 3Ω + 5Ω + 7Ω = 15Ω.

• 4Ω
• 6Ω
• 12Ω
• 18Ω

Answer: 4Ω

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

Answer: In series circuits, components are connected end-to-end, and the same current flows through all. In parallel circuits, components are connected across the same voltage source, allowing multiple paths for current.

This distinction affects how voltage and current are distributed in the circuit.