Edits to “Statement”, “Solution”, “Answer”

igor edited
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revision #18496 parent #18495 ← older
en/11.4.2.md +43 −3
@@ -1,11 +1,51 @@
### Statement
−$11.4.2.$ [Insert the problem statement]
+$11.4.2.$ How should the voltage change in an electrical circuit consisting of a series-connected inductor $L$ and resistance $R$, so that the current in it: (a) increases linearly: $I = \alpha t$? (b) changed sinusoidally: $I = I_0\sin\omega t$?
+
### Solution
−123
+From the Kirchoff's voltage law:
+$$
+iR+L\frac{di}{dt}=u,\tag{1}
+$$
+
+In the case (а):
+
+\begin{gather}
+\alpha tR+L\alpha=u,
+\end{gather}
+
+or equivalently
+
+\begin{gather}
+u=\alpha(Rt+L).
+\end{gather}
+
+In the case (b):
+
+\begin{gather}
+RI_0\sin\omega t + L\omega I_0\cos\omega t=u,
+\end{gather}
+
+or equivalently
+
+\begin{gather}
+u=I_0(R\sin\omega t + L\omega\cos\omega t).
+\end{gather}
+
+
#### Answer
−[Insert a concise answer or boxed result]
+(а)
+
+$$
+u=\alpha(Rt+L);
+$$
+
+(b)
+
+$$
+u=I_0(R\sin\omega t + L\omega\cos\omega t).
+$$