Question

drive the equation of series Resistance and parallel Resistance​

Answer 1

Answer:

According to Ohm's law, the voltage drop, V, across a resistor when a current flows through it is calculated by using the equation V=IR, where I is current in amps (A) and R is the resistance in ohms (Ω). This implies that the total resistance in a series is equal to the sum of the individual resistances.

Explanation:

Answer 2

Hey mate ,

The same current flows through each resistor in series.

Individual resistors in series do not get the total source voltage, but divide it.

The total resistance in a series circuit is equal to the sum of the individual resistances: RN(series)=R1+R2+R3+…+RNRN(series)=R1+R2+R3+…+RN.

Key Terms

series: A number of things that follow on one after the other or are connected one after the other.

resistance: The opposition to the passage of an electric current through that element.

Overview

Most circuits have more than one component, called a resistor, that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance. The simplest combinations of resistors are the series and parallel connections. The total resistance of a combination of resistors depends on both their individual values and how they are connected.

Series Circuits: A brief introduction to series circuit and series circuit analysis, including Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL).

Resistors in Series

Resistors are in series whenever the flow of charge, or the current, must flow through components sequentially.



Resistors in Series: These four resistors are connected in series because if a current was applied at one end, it would flow through each resistor sequentially to the end.

shows resistors in series connected to a voltage source. The total resistance in the circuit is equal to the sum of the individual resistances, since the current has to pass through each resistor in sequence through the circuit.



Resistors connected in a series circuit: Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right).

Using Ohm ‘s Law to Calculate Voltage Changes in Resistors in Series

According to Ohm’s law, the voltage drop, V, across a resistor when a current flows through it is calculated by using the equation V=IR, where I is current in amps (A) and R is the resistance in ohms (Ω).

So the voltage drop across R1 is V1=IR1, across R2is V2=IR2, and across R3 is V3=IR3. The sum of the voltages would equal: V=V1+V2+V3, based on the conservation of energy and charge. If we substitute the values for individual voltages, we get:

V=IR1+IR2+IR3V=IR1+IR2+IR3

or

V=I(R1+R2+R3)V=I(R1+R2+R3)

This implies that the total resistance in a series is equal to the sum of the individual resistances. Therefore, for every circuit with N number of resistors connected in series:

RN(series)=R1+R2+R3+…+RN.RN(series)=R1+R2+R3+…+RN.

Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up.

Since voltage and resistance have an inverse relationship, individual resistors in series do not get the total source voltage, but divide it. This is indicated in an example of when two light bulbs are connected together in a series circuit with a battery. In a simple circuit consisting of one 1.5V battery and one light bulb, the light bulb would have a voltage drop of 1.5V across it. If two lightbulbs were connected in series with the same battery, however, they would each have 1.5V/2, or 0.75V drop across them. This would be evident in the brightness of the lights: each of the two light bulbs connected in series would be half as dim as the single light bulb. Therefore, resistors connected in series use up the same amount of energy as a single resistor, but that energy is divided up between the resistors depending on their resistances.

Resistors in Parallel

The total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances.

LEARNING OBJECTIVES

Calculate the total resistance in the circuit with resistors connected in parallel

KEY TAKEAWAYS

Key Points

The total resistance in a parallel circuit is less than the smallest of the individual resistances.

Each resistor in parallel has the same voltage of the source applied to it (voltage is constant in a parallel circuit).

Parallel resistors do not each get the total current; they divide it (current is dependent on the value of each resistor and the number of total resistors in a circuit).

Key Terms

resistance: The opposition to the passage of an electric current through that element.

parallel: An arrangement of electrical components such that a current flows along two or more paths.

Overview

Resistors in a circuit can be connected in series or in parallel. The total resistance of a combination of resistors depends on both their individual values and how they are connected.

Parallel Circuits: A brief overview of parallel circuit analysis using VIRP tables for high school physics students.

Resistors in Parallel

Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires having negligible resistance. Each resistor thus has the full voltage of the source applied to