L, C and R represents the physical quantities, inductance, capacitance and resistance, respectively. Which of the following combinations have dimensions of frequency?

Question

L, C and R represents the physical quantities, inductance, capacitance and resistance, respectively. Which of the following combinations have dimensions of frequency? (A)  (1/RC)  (B)  R/L  (C)  (1/√LC)  (D)  C/L

Tardigrade Admin · Accepted Answer

Time constant =RC=L/R ∴ (1/RC) and R/L have dimensions of frequency. Also, frequency v=(1/2π √LC) Therefore, (1/√LC) has the dimensions of frequency.

Q. L, C and R represents the physical quantities, inductance, capacitance and resistance, respectively. Which of the following combinations have dimensions of frequency?

$\frac{1}{RC}$

$R / L$

$\frac{1}{L C}$

$C / L$

Time constant $= RC = L / R$ $∴$ $\frac{1}{RC}$ and $R / L$ have dimensions of frequency. Also, frequency $v = \frac{1}{2 π L C}$ Therefore, $\frac{1}{L C}$ has the dimensions of frequency.

Q. L, C and R represents the physical quantities, inductance, capacitance and resistance, respectively. Which of the following combinations have dimensions of frequency?

RC1​

R/L

LC​1​

C/L

Time constant =RC=L/R ∴ RC1​ and R/L have dimensions of frequency. Also, frequency v=2πLC​1​ Therefore, LC​1​ has the dimensions of frequency.

$\frac{1}{RC}$

$R / L$

$\frac{1}{L C}$

$C / L$

Time constant $= RC = L / R$ $∴$ $\frac{1}{RC}$ and $R / L$ have dimensions of frequency. Also, frequency $v = \frac{1}{2 π L C}$ Therefore, $\frac{1}{L C}$ has the dimensions of frequency.