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Express Capacitance In Terms Of Dimensions Of Fundamental Quantities I.e. Mass (m), Length(l), Time(t) And Ampere(a)? |
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Answer» Capacitance(C) is defined as the ability of a electric body to store electric charge. ∴ Capacitance (C) = Total Charge(Q) / potential difference between two plates (V) = COULOMB/ Volt ∵ Volt = Work done (W)/ Charge(q) = Joule/Coulomb ⇒ Capacitance (C) = Charge(q)2/ Work(W) ∵ Charge (q) = Current (I) × Time(t) DIMENSION of [q] = [AT] ———– (I) Dimension of Work = Force × distance = [MLT-2][L] = [ML2T-2] ——— (II) PUTTING values of I and II, [C] = ([AT])2/ [ML2T-2] = [M-1L-2T2+2A2] = [M-1L-2T4A2] Physical Quantities having the same dimensional formula: a. impulse and momentum. b. force, thrust. c. work, energy, TORQUE, moment of force, energy d. angular momentum, Planck’s constant, rotational impulse e. force constant, surface tension, surface energy. f. stress, pressure, modulus of elasticity. g. angular velocity, frequency, velocity gradient h. latent heat, gravitational potential. i. thermal capacity, entropy, universal gas constant and Boltzmann’s constant. j. power, luminous flux. Capacitance(C) is defined as the ability of a electric body to store electric charge. ∴ Capacitance (C) = Total Charge(q) / potential difference between two plates (V) = Coulomb/ Volt ∵ Volt = Work done (W)/ Charge(q) = Joule/Coulomb ⇒ Capacitance (C) = Charge(q)2/ Work(W) ∵ Charge (q) = Current (I) × Time(t) Dimension of [q] = [AT] ———– (I) Dimension of Work = Force × distance = [MLT-2][L] = [ML2T-2] ——— (II) Putting values of I and II, [C] = ([AT])2/ [ML2T-2] = [M-1L-2T2+2A2] = [M-1L-2T4A2] Physical Quantities having the same dimensional formula: a. impulse and momentum. b. force, thrust. c. work, energy, torque, moment of force, energy d. angular momentum, Planck’s constant, rotational impulse e. force constant, surface tension, surface energy. f. stress, pressure, modulus of elasticity. g. angular velocity, frequency, velocity gradient h. latent heat, gravitational potential. i. thermal capacity, entropy, universal gas constant and Boltzmann’s constant. j. power, luminous flux. |
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