Question

Derive an experiment for the equivalent resistance of a combination of a three resistance connected in parallel

Answer 1

Explanation:

■⇨Let's take the above circuit in the experiment so for the equilavent reisitance expression as follows ⇩⇩⇩⇩⇩⇩⇩⇩⇩⇩⇩⇩⇩⇩

●We know the current flowing through all the reisitances is different but te sum of the current flowin through all the resistances is equal to the total current supplies by a battery or cell .

◆So Let I be the total current and the current flowing through R¹ ,R² and R³ be I¹,I² and I³.

•°• I = I¹ + I² + I³.........(1)

Now from ohms law we get :-

→I = V/R.........(2)

Now let's apply ohms law for all the resistances we get;

→I¹=V/R¹........(3)

→I²=V/R².......(4)

→I³=V/R³........(5)

Now put the value of I, I¹,I² and I³ in the first equation

→I = I¹+I²+I³

→V/R= V/R¹ + V/R² + V/R³

→V(1/R) =V (1/R¹ + 1/R² + 1/R³)

cancalling V at both sides -

→1/R=1/R¹ + 1/R² + 1/R³

is the expression for calculation equavelent resistances connected in parallal. ✔✔