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Merge pull request #32 from virtual-labs/dev
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jnipun1994 authored Sep 5, 2024
2 parents a4dc904 + c526881 commit 6fea3d1
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3 changes: 2 additions & 1 deletion experiment/simulation/index.html
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Expand Up @@ -74,6 +74,7 @@
border-radius: 12px;
font-size: 1.1rem;
color: black;
font-weight: 600;
background-image: linear-gradient(
45deg,
#ff512f 0%,
Expand All @@ -88,7 +89,7 @@
@media (min-width: 768px) {
.button-82-front {
font-size: 1.25rem;
padding: 12px 42px;
padding: 0px 55px;
}
}

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38 changes: 30 additions & 8 deletions experiment/theory.md
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Expand Up @@ -60,7 +60,7 @@ $$V_{dc} = \frac {1}{2\pi} \left[\int_{\alpha}^{\pi} V_{max} ~ sin ~ \omega t ~

<center>

$$V_{dc} = \frac {1}{2\pi} [-V_{max} ~ cos \omega t]_{\alpha}^{\pi} = \frac {V_{max} }{2\pi}(1+cos \alpha )........(1)$$
$$V_{dc} = \frac {1}{2\pi}[-V_{max} ~ cos\omega t]_{\alpha}^{\pi} = \frac {V_{max}}{2\pi}(1+cos \alpha)........(1)$$

</center>

Expand Down Expand Up @@ -192,7 +192,21 @@ $$i_o = i_s + i_t =\frac {V_m}{Z} sin(\omega t-\phi) + Ae^{-\left(\frac {R}{L}\r

</center>

Constant A can be obtained from the boundary condition at &omega;t = &alpha;. At time $t = \frac{\alpha}{\omega}$, $i_o = 0$ . Thus from equation (8)
Constant A can be obtained from the boundary condition at &omega;t = &alpha;. At time

<center>

$$t = \frac{\alpha}{\omega}$$

</center>

<center>

$$i_o = 0$$

</center>

Thus from equation (8)

<center>

Expand Down Expand Up @@ -287,9 +301,15 @@ $$i_{s2} = -\left(\frac{E}{R}\right)$$

</center>

The transient current i<sub>t</sub> is given by $i_t = Ae^{-\left(\frac{R}{L}\right)^t}$<br>
The transient current i<sub>t</sub> is given by

<center>

$$i_t = Ae^{-\left(\frac{R}{L}\right)^t}$$

</center>

At &omega;t = &alpha;, $i_o = 0$, i.e., at $t = \frac{\alpha}{\omega}$, $i_o = 0$.
At &omega;t = &alpha;, i<sub>o</sub> = 0, i.e., at t = &alpha;/&omega;, i<sub>o</sub> = 0.

<center>

Expand All @@ -303,7 +323,7 @@ $$i_o =\frac {V_m}{Z}\left[sin(\omega t- \phi )-sin( \alpha - \phi)exp\{-\frac {

</center>

Equation 11 is applicable for &alpha; &le; &omega;t &ge; &beta;. The extinction angle &beta; depends upon load emf E, firing angle &alpha; and the load impedence angle &phi; the average load current $I_o$ is given by<br>
Equation 11 is applicable for &alpha; &le; &omega;t &ge; &beta;. The extinction angle &beta; depends upon load emf E, firing angle &alpha; and the load impedence angle &phi; the average load current i<sub>o</sub> is given by<br>

<center>

Expand All @@ -326,7 +346,7 @@ $$V_o=E\left(1-\frac {\gamma} {2 \pi}\right)+\frac {V_m} {\pi} sin\left(\alpha +
</center>

In case &beta; is made equal to (&gamma;+&alpha;) in the above expression, Equation (15) can be obtained.
If load inductance L is zero in Fig. 5, then extinction angle &beta; = $\theta_2$ and &gamma; = &beta; - &alpha;
If load inductance L is zero in Fig. 5, then extinction angle &beta; = &theta;<sub>2</sub> and &gamma; = &beta; - &alpha;
= &theta;<sub>2</sub> - &alpha; but &theta;<sub>2</sub> = &pi; - &theta;<sub>1</sub>.<br>

This gives &beta; = &theta;<sub>2</sub> = &pi; - &theta;<sub>1</sub> and &gamma; = &pi; - &theta;<sub>1</sub> - &alpha;.
Expand All @@ -343,7 +363,7 @@ as under:<br>

<center>

$$I_{or}=\left[\frac {1}{2 \pi R^2} \int_\alpha ^{\pi-\alpha}\left\{(V_m sin \omega t-E)^2.d(\omega t)\right\}\right]^\frac {1}{2}.........(18)$$
$$I_{or} = \left[\frac {1}{2\pi R^2}\int_\alpha^{\pi-\alpha}\left\{(V_m sin \omega t-E)^2.d(\omega t)\right\}\right]^\frac {1}{2}.........(18)$$

</center>

Expand All @@ -355,9 +375,11 @@ $$P=I^2R+I_oE.......(19)$$

</center>

Supply power factor

<center>

$$Supply~power~factor = I_or^2R+I_o \frac {E}{V_sI_{or}}$$
$$= I_or^2R+I_o \frac {E}{V_sI_{or}}$$

</center>

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