Technical Science - Term 2 - Week 8

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 and designing circuits. The flow of current is driven by voltage, and the relationship between voltage (V), current (I), and resistance (R) is defined by Ohm's Law, which states V = I × R.

Ohm's Law is a fundamental principle in electronics that describes the relationship between voltage, current, and resistance. It can be rearranged to find any of the three variables if the other two are known. For example, if you know the voltage across a resistor and its resistance, you can calculate the current flowing through it. This law is essential for troubleshooting and designing 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 all individual resistances. 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 vital for circuit design and analysis.

Suppose we have a resistor with a resistance of 10 ohms and a voltage of 20 volts applied across it. To find the current, we use Ohm's Law: I = V/R. Substituting the values, we get I = 20V / 10Ω = 2A. This means that a current of 2 amperes flows through the resistor.

Consider a series circuit with three resistors: R1 = 5Ω, R2 = 10Ω, and R3 = 15Ω. The total resistance (R_total) is calculated as R_total = R1 + R2 + R3 = 5Ω + 10Ω + 15Ω = 30Ω. This total resistance affects the current flowing through the circuit.

For a parallel circuit with two resistors, R1 = 6Ω and R2 = 3Ω, the total resistance can be calculated using the formula 1/R_total = 1/R1 + 1/R2. Thus, 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Therefore, R_total = 6/3 = 2Ω. This lower resistance allows more current to flow compared to a series circuit.

Let's work through a problem together. If we have a circuit with a voltage of 12 volts and a resistor of 4 ohms, what is the current? Using Ohm's Law, I = V/R, we substitute the values: I = 12V / 4Ω = 3A. Now, try calculating the current for a voltage of 24 volts across a 6-ohm resistor.

In groups, identify whether the following circuits are series or parallel: Circuit A has two resistors connected end-to-end, while Circuit B has two resistors connected across the same voltage source. Discuss how the current behaves differently in each configuration and how this affects the total resistance.

Consider a circuit with two resistors in series (R1 = 10Ω, R2 = 5Ω) and one resistor in parallel (R3 = 15Ω). First, calculate the total resistance of the series resistors: R_series = R1 + R2 = 10Ω + 5Ω = 15Ω. Then, calculate the total resistance of the parallel resistor with the series combination: 1/R_total = 1/R_series + 1/R3 = 1/15 + 1/15 = 2/15, so R_total = 15/2 = 7.5Ω.

Solve the following problems independently: 1) A circuit has a voltage of 30 volts and a resistance of 10 ohms. Calculate the current. 2) If the current is 5A and the resistance is 2Ω, what is the voltage? Show your calculations.

You have three resistors: R1 = 8Ω, R2 = 12Ω, and R3 = 20Ω connected in series. Calculate the total resistance and the current if the voltage across the circuit is 48 volts.

Given two resistors R1 = 4Ω and R2 = 12Ω in parallel, calculate the total resistance and determine the current if the voltage across the circuit is 24 volts.

• 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).

• The sum of all resistances
• The average of all resistances
• The product of all resistances
• The maximum 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 stays 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.

Answer: 4A

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

Answer: 15Ω

In series, total resistance is the sum: 10Ω + 5Ω = 15Ω.

Answer: 6V

Using Ohm's Law: V = I × R = 2A × 3Ω = 6V.

• Current is the same through all components
• Voltage is the same across all components
• Total resistance is the sum of resistances
• All components must be connected end-to-end

Answer: Voltage is the same across all components

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