Question

34. RLC Series Circuit. In the study of an electrical circuit consisting of a resistor, capacitor, inductor, and an electromotive force (see Figure 4.9), we are led to an initial value problem of the form (20)$$\begin{array}{l}{L \frac{d I}{d t}+R I+\frac{q}{C}=E(t)} \\ {q(0)=q_{0}} \\{I(0)=I_{0}}\end{array}$$ where L is the inductance in henrys, R is the resistance in ohms, C is the capacitance in farads,$$ E(t)$$ is the electromotive force in volts,$$q(t)$$ is the charge in coulombs on the capacitor at time $$t, \text { and } I=d q / d t$$ is the current in amperes. Find the current at time t if the charge on the capacitor is initially zero, the initial current is zero,$$L=10 \mathrm{H}, R=20 \Omega, C=(6260)^{-1} \mathrm{F}$$ and $$E(t)=100 \mathrm{V}$$ [Hint: Differentiate both sides of the differential equation in (20) to obtain a homogeneous linear second-order equation for $$I(t)$$ Then use (20) to determine $$d I / d t \text { at } t=0.1$$

          34. RLC Series Circuit. In the study of an electrical circuit consisting of a resistor, capacitor, inductor, and an electromotive force (see Figure 4.9), we are led to an initial value problem of the form

(20)$$\begin{array}{l}{L \frac{d I}{d t}+R I+\frac{q}{C}=E(t)} \\ {q(0)=q_{0}} \\{I(0)=I_{0}}\end{array}$$

where L is the inductance in henrys, R is the resistance in ohms, C is the capacitance in farads,$$
E(t)$$ is the electromotive force in volts,$$q(t)$$ is the charge in coulombs on the capacitor at time $$t, \text { and } I=d q / d t$$ is the current in amperes. Find the current at time t if the
charge on the capacitor is initially zero, the initial current is zero,$$L=10 \mathrm{H}, R=20 \Omega, C=(6260)^{-1} \mathrm{F}$$ and $$E(t)=100 \mathrm{V}$$ [Hint: Differentiate both sides of the differential equation in (20) to obtain a homogeneous linear second-order equation for $$I(t)$$ Then use (20) to determine $$d I / d t \text { at } t=0.1$$

Added by Eric H.

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