Question

An AC circuit contains resistance of 12Q and inductive reactance 5Q. The phase angle between current and potential difference will be ______.

विकल्प

• `sin^-1 (12/13)`

• `cos^-1 (5/12)`

• `sin^-1 (5/12)`

• `cos^-1 (12/13)`

Answer 1

An AC circuit contains resistance of 12Q and inductive reactance 5Q. The phase angle between current and potential difference will be `underline(cos^-1 (12/13))`.

Explanation:

Given, R = 12 Ω and X_L = 5 Ω

∴ Impedance, Z = `sqrt("R"^2 + "X"^2) = sqrt((12)^2 + (5)^2) = sqrt(144+25)` = 13 Ω

The impedance triangle is as shown below

From this triangle,

cos θ = `"R"/"Z"`

`=> theta = cos^-1 ("R"/"Z") = cos^-1 (12/13)`