Let L denote self inductance of a coil which is in series with a capacitor of capacitance C. Which of the following has unit of second ?

Question

Let L denote self inductance of a coil which is in series with a capacitor of capacitance C. Which of the following has unit of second ? (A) CL (B) L2C2 (C) √ LC (D) C/ L.

Tardigrade Admin · Accepted Answer

[L] = [ML2T-2A-2] [C] = [M-1L-2T4 A2] ∴ [LC] = [T2] ∴ [√LC] = [T] f = (1/T) = (1/2 π √LC) ∴ [T] = [√LC]

Q. Let L denote self inductance of a coil which is in series with a capacitor of capacitance C. Which of the following has unit of second ?

$C L$

$L^{2} C^{2}$

$L C$

$C / L .$

[L] = $[M L^{2} T^{- 2} A^{- 2}]$
[C] = $[M^{- 1} L^{- 2} T^{4} A^{2}]$
$∴ [L C] = [T^{2}] ∴ [L C] = [T]$
$f = \frac{1}{T} = \frac{1}{2 π L C}$
$∴ [T] = [L C]$

Q. Let L denote self inductance of a coil which is in series with a capacitor of capacitance C. Which of the following has unit of second ?

CL

L2C2

LC​

C/L.

[L] = [ML2T−2A−2] [C] = [M−1L−2T4A2] ∴[LC]=[T2]∴[LC​]=[T] f=T1​=2πLC​1​ ∴[T]=[LC​]

$C L$

$L^{2} C^{2}$

$L C$

$C / L .$

[L] = $[M L^{2} T^{- 2} A^{- 2}]$
[C] = $[M^{- 1} L^{- 2} T^{4} A^{2}]$
$∴ [L C] = [T^{2}] ∴ [L C] = [T]$
$f = \frac{1}{T} = \frac{1}{2 π L C}$
$∴ [T] = [L C]$