In an LCR circuit, if ' $V$ ' is the effective value of the applied voltage, $V_R$ is the voltage across '…

In an LCR circuit, if ' $V$ ' is the effective value of the applied voltage, $V_R$ is the voltage across ' $R$ ', ' $\mathrm{V}_{\mathrm{L}}$ ' and ' $\mathrm{V}_{\mathrm{C}}$ ' is the effective voltage across ' L ' and ' C ' respectively then
  1. $\mathrm{V}=\mathrm{V}_{\mathrm{R}}+\mathrm{V}_{\mathrm{L}}+\mathrm{V}_{\mathrm{C}}$
  2. $\mathrm{V}^2=\mathrm{V}_{\mathrm{R}}^2+\mathrm{V}_{\mathrm{L}}^2+\mathrm{V}_{\mathrm{C}}^2$
  3. $\mathrm{V}^2=\mathrm{V}_{\mathrm{R}}^2+\left(\mathrm{V}_{\mathrm{L}}-\mathrm{V}_{\mathrm{C}}\right)^2$
  4. $\mathrm{V}^2=\mathrm{V}_{\mathrm{L}}^2+\left(\mathrm{V}_{\mathrm{R}}-\mathrm{V}_{\mathrm{C}}\right)^2$

Solution


$\therefore \quad \mathrm{V}^2=\mathrm{V}_{\mathrm{R}}^2+\left(\mathrm{V}_{\mathrm{L}}-\mathrm{V}_{\mathrm{C}}\right)^2$ ~

Asked in: MHT CET 2024 (16 May Shift 2)

Practice more AC Circuits questions on Aicharya