1 a set of n identical resistors each of resistance R ohm,when connected in series have effective resistance X ohm - Science - Electricity

Question

1 a set of n identical resistors each of resistance R ohm,when
connected in series have effective resistance X ohm and when
resistors are connected in parallel have effective resistance as Y
ohm Find the relation between R,X&Y
2 a wire of resistance 10 ohm is bent in the form of a closed
circle what is the effecti ve resistance between 2 points at the
ends of any diameter of the circle
3 Define electrical resistivity how is it related 2 electrical
conductivity of the factors length,area of cross-section,nature of
material and temperature which one can control the resistive value
of a conductor

Jyoti Pant · Accepted Answer

1- n number of resistances of R, First connected in series i e $R_{s} = R + R + R + r_{s} = n R = x - - - - - (1)$ Then connected in parallel combination i e $\frac{1}{R_{p}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + = \frac{n}{R} R_{p} = \frac{R}{n} = y --------(2) Comparing (1) and (2), x y = R^{2}$ 2- Resistance of the wire, R = 10 ohm

Both the resistance are in parallel So the equivalent resistance of the wire along the points AB is , $\frac{1}{R_{e q}} = \frac{1}{\frac{R}{2}} \frac{1}{\frac{R}{2}} \frac{1}{R_{e q}} = \frac{1}{5} + \frac{1}{5} = \frac{2}{5} R_{e q} = 2 5 â¢ â€‰ â€‰ â€‰ o h m$ 3- Conductivity: Conductivity is the measure of the ability of a material to conduct electricity It is the inverse of resistivity Its standard unit is mho /m Resistivity: Resistivity is the resistance of a unit length with unit area of cross section of the material of the conductor Unit: ohm-m $Re s i s t i v i t y (ρ) = \frac{R A}{l} E l e c t r i c a l c o n d u c t i v i t y σ = \frac{1}{Re s i s t i v i t y (ρ)}$