The dimension of `frac{R}{L}`where R is resistance and L is Inductance is:
A)`T^(-2)`
B) `T^(-1)`
C) `T^(-1)`
D)`T^(2)`

The unit of L//R is (where L= inductance and R= resistance)

Using method of dimensions, establish the relation among the given quantities. (a) The potential difference V across a conductor depends on current i flowing in it and resistance of conductor R . (b) The speed of light c can be expressed in terms of free space mu_(0) . The energy U stored in an inductor is function of inductance L and current i flowing through it. (d) The time constant tau to R - C circuit can be expressed in terms of resistance R and capacitance. C . Dimensional formulae: V : ML^(2) T^(-3) A^(-1). R: ML^(2) T^(-3) A^(-2) , in_(0) : M^(-1) L^(-3) T^(4) A^(2), mu_(0) : MLT^(-2) A^(2) , L : ML^(2) T^(-2) A^(-2), C : M^(-1) L^(-2) T^(4) A^(2)

The graph shows the variation of l nR v//s (1)/(T^(2)) , where R is resistance and T is temperature. Then find R as function T .

Finding dimensions of resistance R and inductance L, speculate what physical quantities (L//R) and (1)/(2)LI^2 represent, where I is current?

The current in an L - R circuit in a time t = 2L / R reduces to-

Given that in (alpha//pbeta )=alphaz//K_(B)theta where p is pressure, z is distance, K_(B) is Boltzmann constant and theta is temperature, the dimension of beta are (useful formula Energy =K_(B)xx temperature) (A) L^(0)M^(0)T^(0) " " (B)L^(1)M^(-1)T^(2) " " (C)L^(2)M^(0)T^(0)" "(D)L^(-1)M^(1)T^(-2)

A rod of length l with thermally insulated lateral surface is made of a matrical whose thermal conductivity varies as K =C//T where C is a constant The ends are kept at temperature T_(1) and T_(2) The temperature at a distance x from the first end where the temperature is T_(1), T =T_(1)((T_(2))/(T_(1)))^(nx//2l) Find the value of n? .

Let R = K rho^a upsilon^b eta^c D^1 …. (i) where a, b, c are the dimensions and K is dimensionless constant. Writing the dimensions in(i) we get [M^0 L^0 T^0] = [ML^(-3)]^1 (LT^(-1)^b (ML^(-1))^c L^1 = M^(a+c) L^(-3a +b +1-c) T^-b-c Applying the principle of homogeneity of dimensions, we get a +c = 0, c= -a -3a +b +1 -c =0 .... (ii) -b-c = 0 or b= -c From (ii) -3a - c+1 -c = 0 -3a - 2c =-1 or -3a +2a = -1 or a= 1 c = -a =-1, b=-c =1 Putting these values in (i) we get R = K rho^1 upsilon^1 eta^(-1) D^1 R = K (rho upsilonD)/(eta)