physics : class11 Dimensions of Electrical Quantities : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Dimensions of Electrical Quantities
MCQ questions and answers.
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MCQ Questions
1. The dimensions of the quantity e^2/(epsilon_0 hbar), where e is electric charge, epsilon_0 is permittivity of free space, and hbar is reduced Planck's constant, are those of:
A.
Velocity
B.
Acceleration
C.
Electric field
D.
Resistance
Correct Answer:
Velocity
Explanation:
The dimensions are [e^2]/[epsilon_0][hbar] = (I^2T^2)/[(M^-1L^-3T^4I^2)(ML^2T^-1)] = LT^-1, which are the dimensions of velocity.
2. If R is electrical resistance and C is capacitance, the dimensional formula of the product RC is:
A.
ML^2T^-2I^-2
B.
T
C.
T^-1
D.
ML^2T^-3I^-2
Correct Answer:
T
Explanation:
Resistance has dimensions ML^2T^-3I^-2 and capacitance has dimensions M^-1L^-2T^4I^2. Their product is T, the dimension of time.
3. The dimensional formula of the ratio of inductance L to capacitance C is:
A.
M^2L^4T^-6I^-4
B.
M^-2L^-4T^6I^4
C.
ML^2T^-3I^-2
D.
T^2
Correct Answer:
M^2L^4T^-6I^-4
Explanation:
Inductance has dimensions ML^2T^-2I^-2, while capacitance has dimensions M^-1L^-2T^4I^2. Therefore, [L/C] = M^2L^4T^-6I^-4.
4. The dimensions of the ratio of electric field strength E to magnetic field strength B are:
A.
LT^-1
B.
L^-1T
C.
MLT^-2I^-1
D.
T^-1
Correct Answer:
LT^-1
Explanation:
The dimensions of electric field are MLT^-3I^-1 and those of magnetic field are MT^-2I^-1. Their ratio is LT^-1, which has the dimensions of velocity.
5. The dimensional formula of electrical conductivity sigma is:
A.
ML^3T^-3I^-2
B.
M^-1L^-3T^3I^2
C.
M^-1L^-2T^3I^2
D.
ML^-3T^3I^-2
Correct Answer:
M^-1L^-3T^3I^2
Explanation:
Conductivity is the reciprocal of resistivity. Since resistivity has dimensions ML^3T^-3I^-2, conductivity has dimensions M^-1L^-3T^3I^2.
6. The dimensions of the electrical quantity V^2/R, where V is potential difference and R is resistance, are:
A.
ML^2T^-3
B.
ML^2T^-2
C.
MLT^-3I^-1
D.
M^-1L^-2T^3I^2
Correct Answer:
ML^2T^-3
Explanation:
Potential difference has dimensions ML^2T^-3I^-1 and resistance has dimensions ML^2T^-3I^-2. Thus, [V^2/R] = ML^2T^-3, the dimensions of power.
7. The dimensional formula of capacitance per unit length is:
A.
M^-1L^-3T^4I^2
B.
M^-1L^-1T^4I^2
C.
ML^-3T^-4I^-2
D.
M^-1L^-2T^4I^2
Correct Answer:
M^-1L^-3T^4I^2
Explanation:
Capacitance has dimensions M^-1L^-2T^4I^2. Dividing by length introduces an additional L^-1, giving M^-1L^-3T^4I^2.
8. The dimensions of magnetic flux divided by electric charge are equivalent to the dimensions of:
A.
Resistance
B.
Capacitance
C.
Inductance
D.
Conductivity
Correct Answer:
Resistance
Explanation:
Magnetic flux has dimensions ML^2T^-2I^-1 and charge has dimensions IT. Their ratio is ML^2T^-3I^-2, which is the dimensional formula of resistance.
9. Using Coulomb's law in the form E = q/(4pi epsilon_0 r^2), the dimensional formula of electric field E is:
A.
MLT^-3I^-1
B.
ML^2T^-3I^-1
C.
M^-1L^-3T^4I^2
D.
ML^-1T^-2I^-1
Correct Answer:
MLT^-3I^-1
Explanation:
Charge has dimensions IT, permittivity has dimensions M^-1L^-3T^4I^2, and r^2 has dimensions L^2. Hence [E] = IT/([epsilon_0]L^2) = MLT^-3I^-1.
10. If L is inductance and C is capacitance, the dimensions of the quantity 1/square root of (LC) are:
A.
T
B.
T^-1
C.
ML^2T^-3I^-2
D.
ML^-2T^3I^2
Correct Answer:
T^-1
Explanation:
The product LC has dimensions (ML^2T^-2I^-2)(M^-1L^-2T^4I^2) = T^2. Therefore, 1/square root of (LC) has dimensions T^-1.
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