The topic of this problem is energy storage elements. And the problem is to find i(t) in the circuit show below. The circuit is a two node circuit with a node at the top and a node at the bottom, and has a current source i(t), that's the current that we're looking for. It has a capacitor and a resistor as well. We know if we use Kirchhoff's Current Law at the top node, and some of the currents perhaps into that top node, and the sum of those currents is going to be i(t) because i(t) is flowing into that node from the left-hand side. We have minus IC of T And then also minus i sub r of t. And the sum of those is equal to zero, in Kirchhoff's current law. So again we're looking for i(t)t, so if we can find ic(t) and ir(t), then we can solve for i(t). So let's look for ir(t) first. What is ir(t)? ir(t) = V divided by R through Ohm's Law. And our V(t) = 5(1-2e to the -2t), and our resistance is 200 kiloohms. So if we reduce that, we will end up with, 25 * 1- 2e to the minus 2t, and I'll put it into microamps that's our ir(t). That's the first one we need in order to find i(t). the second thing we need to find is we need to find ic(t). In ic(t) Is equal to what? Is equal to C times dv(t), dt. And we know that C is is 10 microfarad so it's 10 times 10 to the minus 6 times the time derivative of v(t)t and v(t) is 5 times 1 minus 2e to the minus 2t So if we continue with that and we've find the derivative, we have (10x10 to the -6), and the derivative of what's inside is going to is give us, 10, that's (-10)(-2)e to the -2t. So ultimately we get an ic(t), which is equal to 200e to the minus 2t micro amps. So if we're looking for i(t), our i(t) is going to be the combination of ir(t) and ir(t). So if we combine those two together we end up with 25 + 150 e to the minus 2t micro amps.