Question

Consider three quantities: `x = (E)/( b) , y = (1)/(sqrt( mu_(0) epsilon _(0))) , and z = (l) /( C R)`.
Here , `l` is the length of a wire , `C` is the capacitance , and `R` is a resistance. All other symbols have usual meanings. Then
A. ` x and y ` have the same dimensions.
B. `x and z` have the same dimensions.
C. `y and z` have the same dimensions.
D. None of the above three pairs have the same dimensions.

Answer 1

Correct Answer - A::B::C
Unit of x `= ("Uit of E")/("Unit of B")` = Unit of velocity
Because `E = vB`
` y = (1)/(sqrt( mu_(0) epsilon _(0)))` = c rarr velocity of light
unit of `z = ("Unit of l")/("Unit of RC") = ("Length")/("Time") = "Velocity"`