The combined resistance of two resistors `R_(1) and R_(1)" is given by "1/R=1/R_(1)+1/R_(2)," where "R_(1)+R_(2) = C` (constant ), show that R is maximum when `R_(1)= R_(2)`.

The combined resistance R of two resistors R_(1) and R_(2) " where " R_(1), R_(2) gt 0 is given by (1)/(R) = (1)/(R_(1)) + (1)/(R_(2)) If R_(1) + R_(2) = C (constant), show that the maximum reistance R is obtained by chossing R_(1) = R_(2)

Calculate equivalent resistance of two resistors R_(1) and R_(2) in parallel where, R_(1) = (6+-0.2) ohm and R_2 = (3+-0.1)ohm

The capacitance of two concentric spherical shells of radii R_(1) and R_(2) (R_(2) gt R_(1)) is

Two resistance R_(1) and R_(2) are made of different material. The temperature coefficient of the material of R_(1) is alpha and of the material of R_(2) is -beta . Then resistance of the series combination of R_(1) and R_(2) will not change with temperature, if R_(1)//R_(2) will not changee with temperature if R_(1)//R_(2) equals

Two resistors of resistance R_(1) and R_(2) having R_(1) gt R_(2) are connected in parallel. For equivalent resistance R, the correct statement is

When resistres of resistyences R_(1)R_(2) and R_(3) are connected in series , then the resistance R_(1) is given by R_(1) = R_(1) + R_(2) +R_(3) In this arrengement the current through each resister is same hut potential difference across then is difference When resitorce of resistance R_(1)R_(2) and R_(3) are connected in particle the effective resistance R_(p) is given by (1)/(R_(p)) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3)) In this arrangement , the potential difference across each resistance is but current through then is difference Read the above passage and answer the following question : (i) Why does the effective resistance increase in series ? (ii) Why does the effective resistance decrease in parallel ? (iii) What basic value are displayed by the above study ?

If equivalent resistances of R _(1) and R _(2) in series and parallel be r _(1) and r _(2) respectively, then (R _(1))/( R _(2)) equals