Units and Dimensions
In the following $$I$$ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:
The dimensional formula of Planck's constant is:
Energy of photon is given as
$$E=h\nu$$
$$\implies h=\dfrac{E}{\nu}$$
Dimension of $$E=[ML^2T^{-2}]$$
Dimension of $$\nu$$ is $$[T^{-1}]$$
Thus the dimension of plank's constant $$h$$ is $$[ML^2T^{-1}]$$
In the following $$I$$ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:
Let $$[\varepsilon _{0}]$$ denote the dimensional formula of the permittivity of vacuum. If $$M=$$ mass, $$L=$$ length, $$T=$$ time and $$A=$$ electric current, then:
If the force is given by $$ F$$ = $$at+bt^2$$ with $$ t $$ as time. The dimensions of a and b are:
The dimensional formula for inductance is:
The dimensions of $${ \left( { \mu }_{ 0 }{ \varepsilon }_{ 0 } \right) }^{ -1/2 }$$ are :
If force $$(F)$$, velocity $$(V)$$ and time $$(T)$$ are taken as fundamental units, the dimensions of mass are
The relation between $$[\in_0]$$ and $$[\mu_0]$$ is
The dimensions of specific resistance are:
What is the dimensions of magnetic field B in terms of C (=coulomb), M, L, T?
The flux of magnetic field through a closed conducting loop changes with time according to the equation,$$ \Phi ={ at }^{ 2 }+bt+c$$.$$(a)$$ Write the $$SI$$ units of $$a,b$$ and $$c$$ $$(b)$$ If the magnitudes of $$a,b$$ and $$c$$ are $$0\cdot 20, 0.40$$ and $$0.60$$ respectively, find the including emf at $$t=2\ s$$.