Technical Science - Term 4 - Week 5

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 load devices (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) flowing 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 the values of voltage, current, and resistance in 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. In contrast, in a parallel circuit, components are connected across the same voltage source, and the total current is the sum of the currents through each component. The total resistance in a parallel circuit can be calculated using the formula: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn.

Consider a circuit with a voltage of 12 volts and a resistance of 4 ohms. To find the current, we can use Ohm's Law: I = V/R. Substituting the values, we get I = 12V / 4Ω = 3A. Therefore, the current flowing through the circuit is 3 amperes.

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. Thus, R_total = 2Ω + 3Ω + 5Ω = 10Ω.

For two resistors in parallel, R1 = 6Ω and R2 = 3Ω, the total resistance can be calculated using the formula: 1/R_total = 1/R1 + 1/R2. Therefore, 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Thus, R_total = 6/3 = 2Ω.

Let's work together on a problem. If a circuit has a voltage of 24 volts and a resistance of 8 ohms, what is the current? Using Ohm's Law, I = V/R, we substitute the values: I = 24V / 8Ω = 3A. Therefore, the current is 3 amperes.

Now, let's find the total resistance of a series circuit with resistors of 4Ω, 6Ω, and 10Ω. We add them together: R_total = 4Ω + 6Ω + 10Ω = 20Ω. The total resistance is 20 ohms.

Consider a parallel circuit with resistors of 12Ω and 4Ω. To find the total resistance, we calculate: 1/R_total = 1/12 + 1/4. This gives us 1/R_total = 1/12 + 3/12 = 4/12. Therefore, R_total = 12/4 = 3Ω.

1. Calculate the current in a circuit with 30 volts and 10 ohms of resistance. 2. Find the total resistance of three resistors in series: 5Ω, 15Ω, and 10Ω. 3. Determine the total resistance of two resistors in parallel: 8Ω and 2Ω. Solve these problems and be prepared to discuss your answers.

Think about how electrical circuits are used in everyday devices. Choose a device, such as a smartphone or a lamp, and describe how understanding circuits and Ohm's Law can help in troubleshooting or improving its design.

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

Answer: V = I × R

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

• The sum of individual resistances
• The product of individual resistances
• The average of individual resistances
• None of the above

Answer: The sum of individual resistances

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

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

Answer: It increases

In a parallel circuit, the total current is the sum of the currents through each branch.

Answer: 4A

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

Answer: 15Ω

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

Answer: 2Ω

Using the formula: 1/R_total = 1/6 + 1/3 = 1/2, thus R_total = 2Ω.

• It doubles
• It halves
• It remains the same
• It quadruples

Answer: It doubles

According to Ohm's Law, if resistance remains constant, doubling the voltage will double the current.