Question

13. (initial value problems) An LC circuit consists of an inductor and capacitor in series. i. Solve the following initial value problem to find $i(t)$ for the LC circuit, $\frac{d^2i}{dt^2} = -284244 \sin(120\pi t + \pi/3)$, $i'(0) = 377$, $i(0) = \sqrt{3}$ ii The differential equation that governs an LC circuit is $\frac{d^2i}{dt^2} + \frac{1}{LC}i = 0$ Use your previous answer to show that the capacitance of the circuit is $C = 14\mu F = 14 \times 10^{-6}F$ if the inductance is $L = 0.5H$. (Hint: you have expressions for $\frac{d^2i}{dt^2}$ and $i$, so try putting them into the differential equation above and solve for C!)

          13. (initial value problems) An LC circuit consists of an inductor and capacitor in series.
i. Solve the following initial value problem to find $i(t)$ for the LC circuit,
$\frac{d^2i}{dt^2} = -284244 \sin(120\pi t + \pi/3)$, $i'(0) = 377$, $i(0) = \sqrt{3}$
ii The differential equation that governs an LC circuit is
$\frac{d^2i}{dt^2} + \frac{1}{LC}i = 0$
Use your previous answer to show that the capacitance of the circuit is $C = 14\mu F = 14 \times 10^{-6}F$ if the inductance
is $L = 0.5H$. (Hint: you have expressions for $\frac{d^2i}{dt^2}$ and $i$, so try putting them into the differential equation
above and solve for C!)

13. (initial value problems) An LC circuit consists of an inductor and capacitor in series.
i. Solve the following initial value problem to find i(t) for the LC circuit,
(d^2i)/(dt^2) = -284244 sin(120π t + π/3), i'(0) = 377, i(0) = √(3)
ii The differential equation that governs an LC circuit is
(d^2i)/(dt^2) + (1)/(LC)i = 0
Use your previous answer to show that the capacitance of the circuit is C = 14μ F = 14 × 10^-6F if the inductance
is L = 0.5H. (Hint: you have expressions for (d^2i)/(dt^2) and i, so try putting them into the differential equation
above and solve for C!)

Added by Jennifer R.

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