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1.Units, Dimensions and Measurement
medium
Dimensions of resistance in an electrical circuit in terms of dimension of mass $M,$ of length $L$ of time $T$ and of current $I$ , would be
A$M^1L^2T^{-2}$
B$M^1L^2T^{-1}I^{-1}$
C$M^1L^2T^{-3}I^{-2}$
D$M^1L^2T^{-3}I^{-1}$
(AIPMT-2007)
Solution
According to Ohm's law
$V = RI\,\,or\,\,R = \frac{V}{I}$
Dimensions of $V = \frac{W}{q} = \frac{{[M{L^2}{T^{ – 2}}]}}{{[IT]}}$
$R = \frac{{[M{L^2}{T^{ – 2}}/IT]}}{{[I]}} = [M{L^2}{T^{ – 3}}{T^{ – 2}}]$
$V = RI\,\,or\,\,R = \frac{V}{I}$
Dimensions of $V = \frac{W}{q} = \frac{{[M{L^2}{T^{ – 2}}]}}{{[IT]}}$
$R = \frac{{[M{L^2}{T^{ – 2}}/IT]}}{{[I]}} = [M{L^2}{T^{ – 3}}{T^{ – 2}}]$
Standard 11
Physics
Similar Questions
Match List $I$ with List $II$
| List $I$ | List $II$ |
| $(A)$ Young's Modulus $(Y)$ | $(I)$ $\left[ M L ^{-1} T ^{-1}\right]$ |
| $(B)$ Co-efficient of Viscosity $(\eta)$ | $(II)$ $\left[ M L ^2 T ^{-1}\right]$ |
| $(C)$ Planck's Constant $(h)$ | $(III)$ $\left[ M L ^{-1} T ^{-2}\right]$ |
| $(D)$ Work Function $(\phi)$ | $(IV)$ $\left[ M L ^2 T ^{-2}\right]$ |
