Physics - Term 2 - Week 7

An electric circuit is a closed loop that allows electric 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 basic principle governing electric circuits is Ohm's Law, which 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.

Ohm's Law is mathematically expressed as V = I × R. This equation allows us to calculate any one of the three variables if the other two are known. For example, if a circuit has a voltage of 12 volts and a resistance of 4 ohms, the current can be calculated as I = V/R = 12V/4Ω = 3A. This relationship is fundamental in circuit analysis and helps in understanding how changing one component affects the entire circuit.

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, 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 essential for predicting how circuits behave under different conditions.

Consider a circuit with a voltage of 24 volts and a resistance of 6 ohms. To find the current, we apply Ohm's Law: I = V/R = 24V/6Ω = 4A. This means that 4 amperes of current flow through the circuit. This example illustrates how to manipulate the formula to find the desired variable.

Suppose we have three resistors in series: R1 = 5Ω, R2 = 10Ω, and R3 = 15Ω. The total resistance can be calculated as R_total = R1 + R2 + R3 = 5Ω + 10Ω + 15Ω = 30Ω. This total resistance affects the current flowing through the circuit when a voltage is applied.

For a parallel circuit with two resistors, R1 = 4Ω and R2 = 12Ω, we calculate the total resistance using the formula 1/R_total = 1/R1 + 1/R2. Thus, 1/R_total = 1/4 + 1/12. Finding a common denominator (12), we get 1/R_total = 3/12 + 1/12 = 4/12. Therefore, R_total = 12/4 = 3Ω.

Let's work through a problem together. A circuit has a voltage of 48 volts and a resistance of 8 ohms. What is the current? Using Ohm's Law, we find I = V/R = 48V/8Ω = 6A. Now, try calculating the current for a circuit with a voltage of 60 volts and a resistance of 15 ohms.

In a series circuit with resistors of 3Ω, 6Ω, and 9Ω, let's calculate the total resistance. R_total = R1 + R2 + R3 = 3Ω + 6Ω + 9Ω = 18Ω. Now, if this circuit is connected to a 36V battery, what is the current? Using I = V/R_total, we find I = 36V/18Ω = 2A.

Consider a parallel circuit with two resistors: R1 = 8Ω and R2 = 4Ω. Calculate the total resistance. Using the formula 1/R_total = 1/R1 + 1/R2, we find 1/R_total = 1/8 + 1/4 = 1/8 + 2/8 = 3/8. Therefore, R_total = 8/3Ω. Now, if this circuit is connected to a 24V battery, calculate the total current flowing through the circuit.

1. A circuit has a voltage of 100 volts and a resistance of 25 ohms. Calculate the current. 2. If the current in a circuit is 10A and the resistance is 5Ω, what is the voltage? 3. A circuit with a 12V battery and a 3Ω resistor is connected. What is the current flowing through the circuit?

1. Calculate the total resistance of a series circuit with resistors of 2Ω, 5Ω, and 8Ω. 2. If this series circuit is connected to a 30V battery, what is the current flowing through the circuit? 3. How would the current change if one of the resistors is removed?

1. For a parallel circuit with resistors of 6Ω and 3Ω, calculate the total resistance. 2. If this circuit is connected to a 12V battery, what is the total current flowing through the circuit? 3. Discuss how adding another resistor in parallel would affect the total resistance and current.

• 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 the resistance.

• R_total = R1 + R2 + R3
• R_total = R1 * R2 * R3
• R_total = 1/R1 + 1/R2 + 1/R3
• R_total = R1 - R2 - R3

Answer: R_total = R1 + R2 + R3

In a series circuit, the total resistance is the sum of all individual resistances.

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

Answer: It decreases

Adding resistors in parallel decreases the total resistance because there are multiple paths for current to flow.

Answer: 4A

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

Answer: 30Ω

R_total = R1 + R2 + R3 = 5Ω + 10Ω + 15Ω = 30Ω.

• 8V
• 6V
• 4V
• 2V

Answer: 8V

Using Ohm's Law, V = I * R = 2A * 4Ω = 8V.

• 2A
• 3A
• 4A
• 6A

Answer: 3A

First, calculate total resistance: R_total = 1/(1/4 + 1/6) = 2.4Ω. Then, I = V/R_total = 12V/2.4Ω = 5A.