Question

derivation for formulae of series connection , parallel connection and series along with parallel connection​

Answer 1

Here is your answer

Hope you will be happy ❤️

The Equation of Resistors in Series.

Since the connection of resistor is in a series fashion that is in the sequential array or continuously one after other. The total resistance is equal to the resistance value of each resistor in the device/ circuit.

Rt= R1+R2+R3+R4+…………………Rn

where

➡️R is the resistance of the resistor .

➡️Rn represents the resistor number or the total resistance value.

➡️Rt is total resistance.

--------------------------------------------------

Resistor in Parallel :-

In this kind of connection, the terminals of resistors are connected to the same terminal of the other resistor to form an electronic circuit/ device.

Resistors are connected is in parallel fashion and hence common voltage drop in the circuit.

Unlike, series connection, in parallel connection, current can have multiple paths to flow through the circuit, hence parallel connection is also current dividers. Common voltage drop is across the parallelly connected circuits/networks. At the terminals of the circuit, the voltage drop is always the same. For example

VR1=VR2=VR3=VRT=14V

The voltage across R1 is equal to the voltage across R2 and similarly, equal to R3 and hence the total voltage drop is equal to the voltage across the circuit. Reciprocal of individual resistance of each resistor and the sum of all the reciprocated resistance of resistor will us the total resistance of the circuit.

1/(Rt) = 1/(R1) + 1/(R2) + 1/(R3) +………… 1(Rn).

hope you happy

Answer 2

Hello my dear friend Namaste,

Your beautiful answer is here:-

For Series Combination:-

The 3 resistances R1, R2 and R3 connected in series. When a potential difference V is applied across the combination, the same current I flows through each resistance.

By Ohm's law, the potential drops across the three resistances are :

V1 = I R1, V2 = I R2, V3 = I R3

If Rs is the equivalent resistance of the series combination, then we must have

V = I R s

But V = sum of the potential drops across the individual resistances

or V = V1 + V2 + V3

or I Rs = I R1 + I R2 + I R3

or Rs = R1 + R2 + R3

For parallel combination:

The 3 resistances R1, R2 and R3 connected in parallel between A and B. Let V be the pot. diff. applied across the combination.

Let I1, I2 and I3 be the currents through the resistances R1, R2 and R3 respectively. Then the current in the main circuit must be I = I1 + I2 + I3

Since, all the resistances have been connected between the same two points A and B, therefore, potential drop V is same across each of them. By Ohm's law, the currents through the individual resistances will be

I1 = V/R1, I2= V/R2, I3 = V/R3

If Rp is the resistance of teh parallel combination, then we must have

I = V/Rp

But, I = I1+ I2 + I3

or V/Rp = V/R1+ V/R2 + V/R3

or 1/Rp = 1/R1 + 1/R2 + 1/R3