A single - phase triac based AC voltage controller feeds a series RL load. The input AC supply is 230 V, 50 Hz. The values of R and L are 10Ω and 18.37 mH, respectively. The minimum triggering angle of the triac to obtain controllable output voltage is

The correct option is 30°.

To find the minimum triggering angle of the triac to obtain a controllable output voltage, we need to calculate the load impedance angle, φ. For a single-phase AC voltage controller feeding a series RL load, the output voltage is controllable only if the triggering angle, α, is greater than or equal to the load impedance angle, φ. If α is less than φ, the triac will conduct continuously (acting like an uncontrolled switch), and control over the output voltage is lost. Therefore, the minimum triggering angle is:

${\alpha }_{\text{min}}=\phi$

The load impedance angle, φ, is given by the formula:

$\phi ={\tan }^{-1}\left(\frac{\omega L}{R}\right)$

First, we calculate the angular frequency, ω, of the AC supply using the frequency, f = 50 Hz:

$\omega =2\pi f$

$\omega =2\times \pi \times 50=100\pi \approx 314.16\text{rad/s}$

Next, we calculate the inductive reactance, X_L = ωL, where L = 18.37 mH = 18.37 × 10^-3 H:

$X_L=314.16\times 18.37\times {10}^{-3}\approx 5.77\Omega$

Now, we substitute the values of X_L and the resistance, R = 10 Ω, into the equation for tan(φ):

$\tan \left(\phi \right)=\frac{X_L}{R}=\frac{5.77}{10}=0.577$

Taking the inverse tangent to solve for the angle φ:

$\phi ={\tan }^{-1}\left(0.577\right)\approx 30°$

Thus, the minimum triggering angle of the triac to obtain a controllable output voltage is 30°.