Surprising as it may seem, the power of a computer is achieved simply by the controlled flow of charges through tiny wires and circuit elements. Chapter Goal: To understand the fundamental physical principles that govern electric circuits.
The equivalent resistance for a group of parallel resistors is A. less than any resistor in the group. B. equal to the smallest resistance in the group. C. equal to the average resistance of the group. D. equal to the largest resistance in the group. E. larger than any resistor in the group.
The equivalent resistance for a group of parallel resistors is A. less than any resistor in the group. B. equal to the smallest resistance in the group. C. equal to the average resistance of the group. D. equal to the largest resistance in the group. E. larger than any resistor in the group.
In this circuit, the battery ideally maintains a voltage between its terminals independent of current drawn. Consequently the capacitor will charge and current flow through the resistor.
In this circuit, the battery ideally maintains a voltage between its terminals independent of current drawn. Consequently, starting from rest, the capacitor will charge and current flow through the resistor.
Charge is conserved and does not accumulate (except on capacitor plates). The electric potential is continuous.
V=IR Neglect internal resistance of the battery and voltage drops along wires. The voltage across the resistor is the battery voltage. Ohm s Law implies I=V/R = 1.5/15 = 0.1 ampere.
The work to move a charge Q through potential difference V is W=QV. The power supplied by a battery driving current I is The units of power are J/s, or W. The power dissipated by a resistor is Or, in terms of the potential drop across the resistor
The power deposited in the filament of a light bulb appears as visible and infrared radiation. 60 Watt If the temperature of the filament exceeds its melting point, the bulb will burn out. A fuse is a resistor designed to burn out at a fixed power and can protect other circuit elements from over voltage.
Household voltage is 120V (rms) 60W = 60J /s = I 2 R = I( IR) = VI I = 60W /120V = 0.5A R = V /I =120V /0.5A = 240Ω 60 Watt Cost 24 hours on requires ( 60J /s)( 24hour) 3600s/hour ( ) = 5,184,000J Note: only 20% of power goes to light! MG&E ~ 13 / kwatt-hour 1kW hour = 1000J /s ( )( 3600s/hour) = 3,600,000J 19 / day 11
Five million joules could lift 100 kg to a height 60 Watt all for pennies! A standard US citizen uses 1 kw. To power 1000 households requires 1 MW. A GW (big) power station provides for 1,000,000 people. 12
Use to make smaller voltage! I 1 = I 2 = I Like summing lengths R R = 2R R = ρ L A
V = V 1 = V 2 I = I 1 + I 2 (lower resistance path has higher current) R R Equivalent Resistance R/2 Add areas R = ρ L A 14
A simple way to make a smaller voltage given a voltage source and two resistors. If a load resistor is connected to point b and its resistance is large compared to R 2, the voltage will be given by the divider formula above.
A real battery loses voltage in proportion to current drawn as if it were an ideal battery in series with an (internal) resistor.
QUESTION:
Kirchoff loop law: ΔV C + ΔV R = 0 Q C C IR = 0 I related to Q C I = dq C dt Q C C + R dq C dt = 0 dq C dt = Q C RC
Basic differential equation Integration to find general solution. dq C dt = Q C RC dq C Q C = 1 RC dt Q Q o dq C Q C = 1 RC Q( t ) t lnq C Q = o RC t Q C t 0 dt ( ) = Q o exp( t /RC) Time constant Charge freely bleeds off/decays exponentially. Similarly, a capacitor charges exponentially with R the internal resistance of the voltage source.
A PMT converts a single photon into a pulse of electrons through cascade electron amplification. The voltage between the photoemitter and the the first plate and between successive plates is ~200 V. A resistor chain is typically used to manufacture the requisite voltages from a single 2 kv power supply. http://sales.hamamatsu.com/en/products/electron-tube-division/detectors/photomultipliertubes.php
A Marx generator switches a set of capacitors connected in parallel to series connection providing voltage addition. http://pagesperso-orange.fr/lyonel.baum/marxgen.jpg, http://en.wikipedia.org/wiki/ Marx_generator
Which of these diagrams represent the same circuit? A. a and b B. b and c C. a and c D. a, b, and d E. a, b, and c
Which of these diagrams represent the same circuit? A. a and b B. b and c C. a and c D. a, b, and d E. a, b, and c