Question

A series L-C-R circuit is connected to a source of alternating emf of 50 V and the potential difference across inductor and capacitor is 90 V and 60 V, respectively. The potential difference across the resistor is ______.

Options

• 70 V

• 60 V

• 40 V

• 80 V

Answer 1

A series L-C-R circuit is connected to a source of alternating emf of 50 V and the potential difference across inductor and capacitor is 90 V and 60 V, respectively. The potential difference across the resistor is 40 V.

Explanation:

Given, V = 50 V, V_L = 90 V, V_c = 60 V

In the L-C-R circuit,

∴ V = `sqrt(V_R^2 + (V_L - V_c)^2)`

⇒ `V^2 = V_R^2 + (V_L - V_c)^2`

`50^2 = V_R^2 + (90 - 60)^2`

⇒ `2500 = V_R^2 + 900 ⇒ V_R^2 = 1600`

⇒ `V_R = sqrt1600` = 40 V