Find the dimension of resistant
Answers
Answer:
Dimensions of L,
M
T
−
2
L
2
A
−
2
Dimensions of R,
M
L
2
T
−
3
A
−
2
Explanation:
Firstly consider resistance.
It's defining equation is, Ohm's law,
V
=
I
R
⇒
R
=
V
I
Now
V
has units of (electric field)*(distance).
But electric field has units (force)/(charge).
Also, charge has dimensions of (current)(time) and force has dimensions (mass)(length)/(time)^2.
Thus, dimensions of
V
is,
[
V
]
=
L
M
L
T
−
2
A
T
⇒
[
V
]
=
M
L
2
T
−
3
A
−
1
Current
I
has dimensions
[
I
]
=
A
Thus, dimensions of resistance,
[
R
]
=
[
V
]
[
I
]
=
M
L
2
T
−
3
A
−
2
For inductance, the defining equation is,
ϕ
=
L
I
But
ϕ
has units (magnetic field)*(length)^2
Magnetic field from Lorentz force law has units, (Force)(velocity)^(-1)(charge)^(-1)
Therefore, dimensions of magnetic field,
[
B
]
=
M
L
T
−
2
L
T
−
1
A
T
⇒
[
B
]
=
M
L
T
−
2
L
A
⇒
[
B
]
=
M
T
−
2
A
−
1
Therefore dimensions of magnetic flux,
[
ϕ
]
=
[
B
]
L
2
⇒
[
ϕ
]
=
M
T
−
2
L
2
A
−
1
Thus finally, dimensions of inductance,
[
L
]
=
[
ϕ
]
[
I
]
⇒
[
L
]
=
M
T
−
2
L
2
A
−
2
Answer:
Resistance = Voltage × Current^(-1)
Resistance = [ML^(2)T^(3)L^(-1)] × L^(-1)
Therefore,
Resistance = ML^(2)T^(3)L^(-2)
• Its unit is ohm.