Question

Complete the steps outlined below for the RLC network shown. 1. Find equations for the network using: Loop 1: voltage law Loop 2: voltage law node: current law 2. Show that the system of differential equations for the currents $i_1$ and $i_2$ in the network can be written as: $L \frac{di_1}{dt} + Ri_2 = E(t)$ $RC \frac{di_2}{dt} + i_2 - i_1 = 0.$ 3. Solve this system () of first order equations for the currents in each branch of the network under the conditions that E=60 volts (constant), L=1 henry, R=50 ohms, C=$10^{-4}$ farad, and $i_1$ and $i_2$ are initially zero. Also solve for $i_3$. Strategy: • Solve the system () of first order equations by eliminating one of the currents and differentiating to obtain a second order differential equation in the other current. • Solve for $i_3$ using the current law at the node. • Clearly show the solution steps for this process and make sure your strategy is clearly outlined using good format and correct notation.

          Complete the steps outlined below for the RLC network shown.
1. Find equations for the network using:
Loop 1: voltage law
Loop 2: voltage law
node: current law
2. Show that the system of differential equations for the currents $i_1$ and $i_2$ in the network can be written as:
$L \frac{di_1}{dt} + Ri_2 = E(t)$
$RC \frac{di_2}{dt} + i_2 - i_1 = 0.$
3. Solve this system (*) of first order equations for the currents in each branch of the network under the
conditions that E=60 volts (constant), L=1 henry, R=50 ohms, C=$10^{-4}$ farad, and $i_1$ and $i_2$ are initially zero.
Also solve for $i_3$.
Strategy:
• Solve the system (*) of first order equations by eliminating one of the currents and differentiating to
obtain a second order differential equation in the other current.
• Solve for $i_3$ using the current law at the node.
• Clearly show the solution steps for this process and make sure your strategy is clearly outlined using
good format and correct notation.

Complete the steps outlined below for the RLC network shown.
1. Find equations for the network using:
Loop 1: voltage law
Loop 2: voltage law
node: current law
2. Show that the system of differential equations for the currents i1 and i2 in the network can be written as:
L (di1)/(dt) + Ri2 = E(t)
RC (di2)/(dt) + i2 - i1 = 0.
3. Solve this system (*) of first order equations for the currents in each branch of the network under the
conditions that E=60 volts (constant), L=1 henry, R=50 ohms, C=10^-4 farad, and i1 and i2 are initially zero.
Also solve for i3.
Strategy:
• Solve the system (*) of first order equations by eliminating one of the currents and differentiating to
obtain a second order differential equation in the other current.
• Solve for i3 using the current law at the node.
• Clearly show the solution steps for this process and make sure your strategy is clearly outlined using
good format and correct notation.

Added by Brenda L.

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