Saved Bookmarks
| 1. |
Across a \( 110 V , 50 Hz \) line, there are connected in series a resistance of \( 200 ohm \), an inductance having a reactance of \( 100 ohm \) and a resistance of \( 40 ohm \) and a capacity of 25 \( \mu F \). Calculate : \( (a) \) the impedance of the circuit, \( (b) \) the current, \( (c) \) the angle by which the current leads or lags the applied e.m.f. |
|
Answer» Given V = 110 V R = 200 Ω XL = 100 Ω XC = 40 Ω f = 50 HZ C = 25 μF (a) Impendence of the circuit \(Z = \sqrt{R^2 + (X_L - X_C)^2}\) \(Z = \sqrt{(200)^2 + (100 - 40)^2}\) \(Z = \sqrt{40000 - 3600}\) \(Z = \sqrt{33700}\) Z = 183.57 Ω (b) Current V = IZ I = V/Z I = \(\frac{110}{183.57}\) I = 0.59 ampere (C) The angle tan ϕ \(=\frac{X_C - X_L}{R}\) \(=\frac{40 - 100}{200}\) \(=\frac{-60}{200}\) tan ϕ \(=\frac{-3}{10}\) \(\phi = tan^{-1}(\frac{-3}{10})\) |
|