Resistors In Series and Parallel Circuits - Keeping It Simple!

Summary

This video walks through the process of calculating the equivalent resistance in a circuit involving resistors in series and parallel. It explains how to simplify the circuit, use Ohm’s Law to calculate current, and determine the voltage drops across resistors. The video also covers how to compute power absorption for each resistor and verify the law of conservation of energy by comparing the power delivered by the battery with the total power absorbed by the resistors.

Takeaways

• 😀 Redraw the circuit for clarity: Label key points A, B, and C, and identify the battery's positive and negative terminals.
• 😀 The circuit consists of a 20 ohm resistor and a 5 ohm resistor in parallel, both meeting at point B, and a 6 ohm resistor in series with the parallel combination.
• 😀 The equivalent resistance of the parallel resistors (20 ohms and 5 ohms) is calculated using the formula 1/R_eq = 1/20 + 1/5, which equals 4 ohms.
• 😀 The total resistance of the circuit is the sum of the series resistors: 6 ohms + 4 ohms = 10 ohms.
• 😀 Using Ohm’s law (V = IR), the total current is calculated by dividing the battery voltage (20V) by the total resistance (10 ohms), resulting in 2 amps.
• 😀 The total current of 2 amps splits between the 20 ohm and 5 ohm resistors, with more current flowing through the 5 ohm resistor because of its lower resistance.
• 😀 A formula can be used to calculate the current through each resistor in parallel: I_r1 = (total current * R2) / (R1 + R2). This gives 0.4 amps for the 20 ohm resistor and 1.6 amps for the 5 ohm resistor.
• 😀 An alternative method to calculate the currents involves calculating the voltage drop across the resistors. For the 6 ohm resistor, the voltage drop is 12V, leaving 8V across the parallel resistors.
• 😀 Using the voltage drop, the current through each resistor in parallel is calculated: 0.4 amps through the 20 ohm resistor and 1.6 amps through the 5 ohm resistor.
• 😀 The power absorbed by each resistor can be calculated: 3.2W for the 20 ohm resistor, 12.8W for the 5 ohm resistor, and 24W for the 6 ohm resistor, with a total power of 40W, which matches the power delivered by the battery, adhering to the law of conservation of energy.

Q & A

What is the first step in solving the circuit problem?

The first step is to redraw the circuit and label the points, starting with point A for the positive terminal, point B as the meeting point for two resistors, and point C for the negative terminal.

How do you calculate the equivalent resistance of the two resistors in parallel?

To calculate the equivalent resistance of the 20 ohm and 5 ohm resistors in parallel, you use the formula: 1 / (1/20 + 1/5), which simplifies to 4 ohms.

What is the total resistance of the circuit?

The total resistance is the sum of the equivalent resistance (4 ohms) from the parallel resistors and the 6 ohm resistor in series, which gives a total resistance of 10 ohms.

How is the total current in the circuit calculated?

The total current is calculated using Ohm's Law, which states V = IR. The current is the voltage of the battery (20V) divided by the total resistance (10 ohms), resulting in a current of 2 amps.

Why does more current flow through the 5 ohm resistor than the 20 ohm resistor?

According to Ohm's Law, a lower resistance allows more current to flow. Since the 5 ohm resistor has less resistance than the 20 ohm resistor, more current flows through it.

What is the relationship between the current through the 5 ohm resistor and the 20 ohm resistor?

Since the 20 ohm resistor is four times the value of the 5 ohm resistor, the current through the 5 ohm resistor will be four times greater than the current through the 20 ohm resistor.

How can you calculate the current through the 5 ohm and 20 ohm resistors using a formula?

To calculate the current through each resistor in parallel, you can use the formula: I1 = (Total Current * R2) / (R1 + R2) and I2 = (Total Current * R1) / (R1 + R2), where R1 and R2 are the resistances of the two resistors.

How is the current through the 5 ohm resistor calculated?

The current through the 5 ohm resistor is calculated as (Total Current * R2) / (R1 + R2), where R1 is 20 ohms, R2 is 5 ohms, and the total current is 2 amps, resulting in a current of 0.4 amps through the 5 ohm resistor.

How is the current through the 20 ohm resistor calculated?

The current through the 20 ohm resistor is calculated as (Total Current * R1) / (R1 + R2), where R1 is 20 ohms, R2 is 5 ohms, and the total current is 2 amps, resulting in a current of 1.6 amps through the 20 ohm resistor.

How can the power absorbed by each resistor be calculated?

The power absorbed by each resistor is calculated using different formulas. For the 20 ohm resistor: P = I² * R (0.4² * 20 = 3.2 watts), for the 5 ohm resistor: P = V * I (8V * 1.6A = 12.8 watts), and for the 6 ohm resistor: P = V² / R (12V² / 6 ohms = 24 watts).

How does the total power delivered by the battery compare to the power absorbed by the resistors?

The total power delivered by the battery is 40 watts (V * I = 20V * 2A). When you add the power absorbed by the resistors (3.2W + 12.8W + 24W), it also equals 40 watts, demonstrating the law of conservation of energy.