3. Kirchhoff's voltage laws tell us that (1) At any node (or junction), the sum of currents flowing into that node is equal to the sum of currents flowing out of that node, and (2) the net voltage drop around each closed loop is zero. In addition to Kirchhoff's laws, we also have the relation between the current I(t) in amperes through each circuit element and the voltage drop v(t) in volts across the element: = Ri, R = resistance in ohms; V Cd = i, Latit = v₂ C = capacitance in farads L = inductance in henries. Consider the circuit shown below. Use the voltage laws and current relationship to show that the current i across the inductor and the voltage v across the capacitor satisfy the differential equations (you may need problem 27 from the 3.2 in the book as reference): di dt =-i-v R = 2 ohm dv dt = 2i - v R = 1 ohm www C=0.5 F L=1H
3. Kirchhoff's voltage laws tell us that (1) At any node (or junction), the sum of currents flowing into that node is equal to the sum of currents flowing out of that node, and (2) the net voltage drop around each closed loop is zero. In addition to Kirchhoff's laws, we also have the relation between the current I(t) in amperes through each circuit element and the voltage drop v(t) in volts across the element: = Ri, R = resistance in ohms; V Cd = i, Latit = v₂ C = capacitance in farads L = inductance in henries. Consider the circuit shown below. Use the voltage laws and current relationship to show that the current i across the inductor and the voltage v across the capacitor satisfy the differential equations (you may need problem 27 from the 3.2 in the book as reference): di dt =-i-v R = 2 ohm dv dt = 2i - v R = 1 ohm www C=0.5 F L=1H
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Transcribed Image Text:3. Kirchhoff's voltage laws tell us that (1) At any node (or junction), the sum of
currents flowing into that node is equal to the sum of currents flowing out of that
node, and (2) the net voltage drop around each closed loop is zero. In addition to
Kirchhoff's laws, we also have the relation between the current I(t) in amperes
through each circuit element and the voltage drop v(t) in volts across the element:
= Ri, R = resistance in ohms;
V
i,
v₂
Cd dv
dt
L
di
dt
=
-
C = capacitance in farads
L = inductance in henries.
Consider the circuit shown below. Use the voltage laws and current relationship to
show that the current i across the inductor and the voltage v across the capacitor
satisfy the differential equations (you may need problem 27 from the 3.2 in the book
as reference):
di
dt
== - v
R = 2 ohm
dv
dt
= 2i - v
R = 1 ohm
C = 0.5 F
L = 1 H
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