AP EAMCET · PHYSICS · Units and Dimensions
The expressions below give current \(I\) through an electronic component as a function of applied potential \(V . I_0\) and \(V_0\) are constants having dimensions of current and potential respectively. Which of the following are dimensionally incorrect?
(A) \(I=I_0\left(e^{\frac{2 V}{V_0}}+1\right)\)
(B) \(I=I_0\left(e^{\frac{v}{2 V_0}}-1\right)\)
(C) \(I=I_0 V_0\left(e^{\frac{V}{V_0}}-1\right)\)
(D) \(I=I_0\left(\frac{V}{V_0}\right)\left(e^{\frac{V}{V_0}}-1\right)\)
- A \(\mathrm{A}\)
- B \(\mathrm{B}\)
- C \(\mathrm{C}\)
- D \(\mathrm{D}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{C}\)
Step-by-step Solution
Detailed explanation
According to the principle of homogeneity, a physical equation will be dimensionally correct only if the dimensions of all the terms occuring on both side of the equation are the same. Hence, in option (c) \(I=I_0 V_0\left(e^{\frac{v}{V_0}}-1\right)\) Dimension of \(I \neq\)…
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