Question

A battery is charged by $a1-\varphi$ one pulse thyristor controlled rectifier. The supply is 30 V, 50Hz and battery emf is constant at 10V. The value of resistance required to be added in series with battery to limit the charging current to 4 A with assumption that SCR is triggered continuously and it has a voltage drop of 1V across it is

• A. $2.10\Omega$
• B. $10.42\Omega$
• C. $4.24\Omega$
• D. $24.10\Omega$

Answer 1

The correct option is A $2.10\Omega$

Given, SCR voltage drop = 1V

Assuming current flowing in battery be $i_0$

Writing KVL in loop,

$V_m\sin \omega t=E+i_{0}R+\text{drop across SCR}$

$=E+i_{0}R+1$

$i_0=\frac{V_m\sin \omega t-(E+1)}{R}$

SCR is turned on when,

$V_m\sin {\theta }_1=E+1$

SCR is turned off when,

$V_m\sin {\theta }_2=E+1$

and ${\theta }_2=\pi -{\theta }_1$

${\theta }_1={\sin }^{-1}\left(\frac{E+1}{V_m}\right)={\sin }^{-1}\left(\frac{11}{30}\right)={21.51}^{\circ }$

The battery charging requires only average current,

$I_0=\frac{1}{2\pi R}[{\int }_{{\theta }_1}^{\pi -{\theta }_1}{V}_m\sin \omega t-(E+1\left)d\omega t\right]$

$=\frac{1}{2\pi R}\left[\right(-V_m\cos \omega t{)}_{{\theta }_1}^{\pi -{\theta }_1}-{\left\{\right(E+1\left)\omega t\right\}}_{{\theta }_1}^{\pi -{\theta }_1}]$

$=\frac{1}{2\pi R}[-V_m(\cos (\pi -{\theta }_1)-\cos {\theta }_1)-(E+1\left)\right(\pi -2{\theta }_1\left)\right]$

$=\frac{1}{2\pi R}\left[V_m\right(\cos {\theta }_1+\cos {\theta }_1)-(E+1\left)\right(\pi -2{\theta }_1\left)\right]$

$I_0=\frac{1}{2\pi R}[2V_m\cos {\theta }_1-(E+1\left)\right(\pi -2{\theta }_1\left)\right]$

For charging current , $I_0=4A$

$R=\frac{1}{2\pi I_0}[2V_m\cos {\theta }_1-(E+1\left)\right(\pi -2{\theta }_1\left)\right]$

$=\frac{1}{2\pi \times 4}[2\times \sqrt{2}\times 30\times \cos ({21.51}^{\circ })-(10+1\left)(\pi -{43}^{\circ }\times \frac{\pi }{180})\right]$

$=\frac{1}{8\pi }[78.94-26.3]=2.09\Omega =2.10\Omega$