Update lecture-09.html

jcponce · Aug 2, 2023 · ae3a858 · ae3a858
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Showing 1 changed file with 70 additions and 2 deletions.
diff --git a/math1052/lecture-09.html b/math1052/lecture-09.html
@@ -133,11 +133,77 @@ <h4>1 Ordinary Differential Equations</h4>
 						<p><strong>1.6.2 Worked-out example: RL circuit</strong></p>
 					</div>
 
-					<div style="margin-top: -35px;" >
+					<div class="size-80"  style="margin-top: -10px;" >
+						<div class="left-txt">
+
+							<p>
+								<span>The voltage drop due to the inductor is $\ds L\dif{J}{t}$ where $L$ is
+									the inductance (in Henries).
+								</span>
+							</p>
+						</div>
+					</div>
+
+
+					<div class="size-85"  style="margin-top: 0px;" >
+						<div class="left-txt">
+
+							<p>
+								<span>According to <span id="rr">Kirchhoff's Law</span> the sum of the voltage drops is equal
+									to the supplied voltage $E(t)$ (in Volts).
+								</span>
+								<span class="fragment" data-fragment-index="0">
+									Hence
+								</span>
+							</p>
+						</div>
+						<div>
+							<p>
+								<span class="fragment" data-fragment-index="0">
+									$\ds L\dif{J}{t}+RJ=E(t). \qquad (*)$
+								</span>
+							</p>
+						</div>
+					</div>
+
+					<div style="margin-top: -40px;" >
 						<img style="width: 30%;" src="images/lect-09/circuit.png">
 					</div>
+
+
+					<br/><br/><br/>
+				</section>
+
+			</section>
+
+			<section>
+
+				<section data-auto-animate>
+					<h4>1 Ordinary Differential Equations</h4>
+					<div id="sbt">
+						<p><strong>1.6.2 Worked-out example: RL circuit</strong></p>
+					</div>
+
+					<div class="size-80"  style="margin-top: -10px;" >
+						<div class="left-txt">
+
+							<p>
+								<span>
+									<strong>
+										Example: 
+									</strong>
+									Suppose in an RL circuit a battery supplies a
+									constant voltage of 80V, the inductance is 2H and the resistance is
+									$10\Omega$.
+									(i) Find an expression for $J(t),$ and (ii)
+									determine the the current after 1 second if $J(0)=0.$
+								</span>
+							</p>
+						</div>
+					</div>
+
 
-					<div class="size-85"  style="margin-top: -35px;" >
+					<div class="size-85"  style="margin-top: 0px;" >
 						<div class="left-txt">
 
 							<p>
@@ -157,6 +223,8 @@ <h4>1 Ordinary Differential Equations</h4>
 							</p>
 						</div>
 					</div>
+
+
 
 
 					<br/><br/><br/>