Electric Circuits and Current

Circuits Power Source: provides current and voltage to parts of a circuit Switch: controls current flow in a circuit Circuits Resistor: provides electrical resistance to reduce current flow or control signal levels Capacitor: stores electric charge Inductor: induces magnetic field when current flows through the coil. Simple Circuit with Resistor Everything has a natural electrical resistance, including copper wire; however, the resistance of copper wire is extremely low, making it a good conductor of electricity. Voltage and current are usually good indicators of how strong a power supply is, and they are directly proportional: V = I · R, where V is voltage measured in Volts, I is current measured in Amperes or Amps and R is resistance measured in Ohms. Simple Circuit with Resistor The relationship V = IR is important. Batteries come with a predetermined voltage. If you hook up the two leads of a battery with a copper wire, it is going to get REALLY HOT. This is because copper wire has a really low resistance, thus your current I = VR is going to be really huge, which means energy is going to get converted into heat. Thus, resistors are often used to control how much current is being supplied to the rest of the circuit. V = IR = VR Capacitors Remember that capacitors store charge, and the amount of voltage in a capacitor is directly proportional to the amount of charge it has currently stored. Current is just the rate of change of charge, i.e. it is how much charge that is travelingR past a point in a given t time frame. Thus, I = dq dt implies q(t) = 0 I (t) dt. Thus, Z 1 1 s VC (t) = qC (t) = I (s) dt. C C 0 where C is called the capacitance (measured in farads). Since VC cannot exceed the voltage of the battery, this means at some point VC (t) must level off, i.e. Z 1 ∞ V = lim VC (t) = I (s) ds. t→∞ C 0 RC Circuit V V 0 0 I (t) I (t) = VR (t) + VC (t) Z 1 t I (s) ds = R · I (t) + C 0 dI 1 = R· + · I (t) dt C dI 1 = + I (t) dt RC = I0 e −t/(RC ) V −t/(RC ) = e R Inductors Because of the geometry of inductors, when a fluctuating current flows through an inductor, it induces a new current that runs opposite to the current flow from the power supply. This mechanism is often used to block AC current in electronics. VL (t) = L dI dt RL Circuits V (t) = VR (t) + VL (t) dI V (t) = R · I (t) + L dt V (t) dI R = + · I (t) L dt LZ V (t) Rt/L e dt I (t) = e −Rt/L L RLC circuit V (t) = VL + VR + VC Z dI 1 t V (t) = L · + R · I (t) + I (s) ds dt C 0 1 V 0 (t) = L · I 00 (t) + R · I 0 (t) + I (t) C