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If C, R, L and I denote Capacity, Resist...

If C, R, L and I denote Capacity, Resistance, Inductance and Electric current respectively, the quantities having the same dimensions of time are
(i)CR (ii)`L/R`
(iii)`sqrt(LC)` (iv)`LI^(2)`

A

(1) and (2) only

B

(1) and (3) only

C

(1) and (4) only

D

(1),(2) and (3) only

Text Solution

Verified by Experts

The correct Answer is:
D
(A) Planck's constant = Energy/Frequency `= [ML^(2)T^(-2)]/[T^(-1)] = [ML^(2)T^(-3)]`
(B) Gravitational constant = ` Fr^(2)/m_(1)m_(2) = [MLT^(-2)][L^(2)] = [M^(-1)L^(3)T^(-2)]`
( C) Bulk modulus = Bulk stress/Volume strain =` (F//A)/dv/v = [ML^(-1)T^(-2)]`
(D) Co-efficient of viscocity = `[F]/(A.(dv/dx)) = [MLT^(-2)]/(L^(2)[LT^(-1)/L]) = [ML^(-1)T^(-1)]`
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Knowledge Check

  • If L, C, R represent inducatance, capaitance and resistance respectively, the combinations having dimensions of requency are :

    A
    `(1)/(sqrt(LC))`
    B
    `(L)/(C )`
    C
    `(R )/(L)`
    D
    `(R )/(C )`

  • If M, L, T and I stand for Mass, Length, Time and electric current respectively, the dimensional formula for Capacitance is

    A
    `[M^(-1)L^(2)T^(-4)I^(2)]`
    B
    `[M^(-1)L^(-2)T^(4)I^(2)]`
    C
    `[ML^(2)T^(4)I^(2)]`
    D
    `[ML^(2)T^(-4)I^(-2)]`

  • The ratio L//R , where L and R stand for Inductance and Resistance, has the same dimensions as those of

    A
    Velocity
    B
    Acceleration
    C
    Time
    D
    Force

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