## Calculating Resistance in Parallel and Series: Questions for Secondary School

In this article, we will discuss how to calculate resistance in parallel and series circuits. We will also provide some practice questions for secondary school students.### Calculating Resistance in Parallel

When resistors are connected in parallel, the total resistance is less than the resistance of any individual resistor. This is because the current can flow through multiple paths, so each resistor has less resistance to the flow of current. The formula for calculating the total resistance of a parallel circuit is: ``` Rt = 1 / (1/R1 + 1/R2 + ... + 1/Rn) ``` where: *### Rt

is the total resistance of the circuit *### R1

,### R2

, ...,### Rn

are the resistances of the individual resistors For example, if you have two resistors connected in parallel with resistances of 10 ohms and 20 ohms, the total resistance of the circuit would be: ``` Rt = 1 / (1/10 + 1/20) = 6.67 ohms ```### Calculating Resistance in Series

When resistors are connected in series, the total resistance is greater than the resistance of any individual resistor. This is because the current has to flow through all of the resistors, so each resistor adds to the overall resistance of the circuit. The formula for calculating the total resistance of a series circuit is: ``` Rt = R1 + R2 + ... + Rn ``` where: *### Rt

is the total resistance of the circuit *### R1

,### R2

, ...,### Rn

are the resistances of the individual resistors For example, if you have two resistors connected in series with resistances of 10 ohms and 20 ohms, the total resistance of the circuit would be: ``` Rt = 10 + 20 = 30 ohms ```### Practice Questions

1. A circuit has two resistors connected in parallel with resistances of 10 ohms and 20 ohms. What is the total resistance of the circuit? 2. A circuit has two resistors connected in series with resistances of 10 ohms and 20 ohms. What is the total resistance of the circuit? 3. A circuit has three resistors connected in parallel with resistances of 10 ohms, 20 ohms, and 30 ohms. What is the total resistance of the circuit? 4. A circuit has three resistors connected in series with resistances of 10 ohms, 20 ohms, and 30 ohms. What is the total resistance of the circuit? 5. A circuit has four resistors connected in parallel with resistances of 10 ohms, 20 ohms, 30 ohms, and 40 ohms. What is the total resistance of the circuit? 6. A circuit has four resistors connected in series with resistances of 10 ohms, 20 ohms, 30 ohms, and 40 ohms. What is the total resistance of the circuit?### Answers

1. 6.67 ohms 2. 30 ohms 3. 11.11 ohms 4. 60 ohms 5. 13.33 ohms 6. 120 ohmsChapter 23 Series And Parallel Circuits

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