Name: Introduction to Electric Charge
Uploaded: 2019-07-19
Duration: 9 min 41 s
Description: In this video, we will study electric charge and its properties and we will also learn about different methods of charging.

Question

With the help of a circuit diagram derive the formula for the resultant resistance of three resistances connected in series.

Accepted Answer

If the resistances are connected end to end and same current flows through each resistor then combination of resistances are called series combination.

Let, three resistances $R_{1,} R_{2}$ and $R_{3}$ be connected in series. Let the current flowing through them be $I$ . According to Ohm's law, the voltage $V_{1}, V_{2}$ and $V_{3}$ across $R_{1}, R_{2}$ and $R_{3}$ respectively will be given as:

$V_{1} = I R_{1}$ ,

$V_{2} = I R_{2}$ ,

$V_{3} = I R_{3}$ .

The sum of the potential difference across each resistor is given by $V = V_{1} + V_{2} + V_{3}$ .

So, $V = I R_{1} + I R_{2} + I R_{3} . . . . . . . . . . (1)$ .

The effective resistor is a single resistor, which can replace the resistors effectively, so as to allow the same current through the electric circuit. Let the effective resistance of the series-combination of the resistors, be $R_{s}$ . Then,

$V = I R_{s} . . . . . . . . . . (2)$ .

On combining equations $(1)$ and $(2)$

$I R_{s} = I R_{1} + I R_{2} + I R_{3} R_{s} = R_{1} + R_{2} + R_{3}$

Thus, when number of resistors are connected in series, then their equivalent resistance and effective resistance is equal to the sum of the individual resistances.

With the help of a circuit diagram derive the formula for the resultant resistance of three resistances connected in series.

Important Questions on Electricity

Learn and Prepare for any exam you want !