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4 MA 36600 LECTURE NOTES: MONDAY, MARCH 9 Figure 4. Graph of Solution u ( t ) = u c ( t ) + U ( t ) under Resonance 0 2.5 5 7.5 10 12.5 15 17.5 20 -20 -16 -12 -8 -4 4 8 12 16 20 ii. Ohm’s Law asserts that the voltage across a resistor is proportional to the current: V resistor I = V resistor = I R for some positive constant R . We call R the resistance ; it is measured in ohms. iii. The voltage across a capacitor is proportional to the charge: V capacitor Q = V capacitor = 1 C Q for some positive constant C . We call C the capacitance ; it is measured in farads. iv. The voltage in the battery is a function of time: V battery = E ( t ) . We call such an electrical circuit an RLC Circuit . We have chosen our units so that 1 volt = 1 henry × 1 ampere sec = 1 ampere × 1 ohm = 1 farad 1 × 1 coulomb . We think of voltage V as being similar to force F . Just as Newton’s Second Law of Motion states that F = m a is the sum of the forces on an object,

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