A 750 Hertz – 20 volt source is connected to a resistance of 100 ohm, an inductance of 0.1803 henry and a capacitance of 10μf, all in series. What is the time in which…

Q: A 750 Hertz – 20 volt source is connected to a resistance of 100 ohm, an inductance of 0.1803 henry and a capacitance of 10μf, all in series. What is the time in which the resistance (Thermal capacity = 2 joule/°C) will get heated by 10 °C?

Sol: Here, f = 750 Hz, Ev = 20 V , R = 100 Ω

L = 0.1803 H, C = 10 μF = 10-5 F , t = ?

∆θ = 10 °C, thermal capacity = 2 J/ °C

XL = ωL = 2 π f L = 2 × 3.14 × 750 × 0.1803

≈ 850 ohm

$\large X_C = \frac{1}{\omega C} = \frac{1}{2 \pi f C} $

$\large = \frac{1}{2 \pi \times 750 \times 10^{-5}} $

= 21.2 ohm

$\large Z = \sqrt{R^2 + (X_L – X_C)^2}$

$\large Z = \sqrt{100^2 + (850 – 21.2)^2}$

= 835 ohm

Power dissipated , $\large = E_v I_v cos\phi $

$\large = E_v (\frac{E_v}{Z}) \frac{R}{Z} = \frac{20^2 \times 100}{835}$

= 0.0574 W