23 Capacitors

This page covers the capacitors section of the course. One crucial part of this section is the ability to understand how to take Ln on an expoential function. You must make sure you work this out before you start the decay part. Also there are some tricky formulae again so you must make sure you make notes and go back to them to check what each thing is and when it applies. A capacitor has a current which changes all the time (unless charged with a constant current) so the formula are all time based.

Resources

23 Capacitors Student Booklet

23 Capacitors Part B

23 Capacitors Part A

23.3 Challenge Sheet Flash

23.3 HSW Capacitor Planning Datalogging

23.3 Support worksheet capacitor graph

Picoscope Capacitor Decay

Capacitor Decay 47k 2200mF

Natural Logarithms

This algebra video tutorial provides a basic introduction into natural logarithms. It explains how to evaluate natural logarithmic expressions with the natural base e and how to evaluate exponential ...expressions with natural logs in on the exponent of the natural base e using properties of logarithms.

Algebra For Beginners: https://www.youtube.com/watch?v=MHeirBPOI6w
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Fractions - Basic Introduction: https://www.youtube.com/watch?v=GvLIEiqxS6s
Linear Equations - Test Review: https://www.youtube.com/watch?v=Ft2_QtXAnh8
How To Factor Trinomials: https://www.youtube.com/watch?v=-4jANGlJRSY
Systems of Linear Equations - 2 Variables: https://www.youtube.com/watch?v=oKqtgz2eo-Y
Quadratic Equations - Test Review: https://www.youtube.com/watch?v=fFFA7Q4eVuY
Multiplying Rational Expressions: https://www.youtube.com/watch?v=RROSgr4oXjU
Graphing Rational Functions: https://www.youtube.com/watch?v=bWVhwYdSnfk
Radical Expressions - Test Review: https://www.youtube.com/watch?v=wOcc5EoOojE
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Logarithms - The Easy Way! https://www.youtube.com/watch?v=kqVpPSzkTYA
Log to Exponential Form: https://www.youtube.com/watch?v=f0C1KL7GkqY
Change of Base Formula: https://www.youtube.com/watch?v=FFm-zaFW_X4
Change of Base Log Problem: https://www.youtube.com/watch?v=p7hD9VdXv9U
Properties of Logarithms: https://www.youtube.com/watch?v=Jtv9Lnf7Zw8
Expanding Logarithmic Expressions: https://www.youtube.com/watch?v=OIz-5MyJA3g
Condensing Logarithmic Expressions: https://www.youtube.com/watch?v=luRrOlsB4cY
Natural Logarithms: https://www.youtube.com/watch?v=daUlTsnCNRQ
Solving Exponential Equations: https://www.youtube.com/watch?v=9tutJ5xrRwg
Exponential Equations - Quadratic Formula: https://www.youtube.com/watch?v=1_XHAzgUi1o
Exponential Equations - Quadratic Form: https://www.youtube.com/watch?v=yNgmVu0R_T8
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Solving Logarithmic Equations: https://www.youtube.com/watch?v=fnhFneOz6n8
Logarithmic Equations - Harder Examples: https://www.youtube.com/watch?v=PIx0Z0LqqFY
Logarithmic Equations - Different Bases: https://www.youtube.com/watch?v=XvwPB21Gm9A
Exponential Logarithmic Equations: https://www.youtube.com/watch?v=6CrXFvvwsaE
Graphing Logarithmic Functions: https://www.youtube.com/watch?v=-nptxS9rZNA
Graphing Exponential Functions: https://www.youtube.com/watch?v=DASfP8KAyvs
Graphing Natural Log Functions: https://www.youtube.com/watch?v=ymXD6xCmzJE
Compound Interest Word Problems: https://www.youtube.com/watch?v=Hn0eLcOSQGw
Interest Compounded Continuously: https://www.youtube.com/watch?v=Ln97Hd7AiDc
Population Growth Word Problems: https://www.youtube.com/watch?v=k4LLdFFLRmQ
Logarithms Practice Problems: https://www.youtube.com/watch?v=7DVbQKI600k
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Where does "e" come from? https://www.youtube.com/watch?v=pDFcu_wLOzo
Complex Logarithmic Equations: https://www.youtube.com/watch?v=k7m2z0bX_tg
Exponential Equations - Powers of X: https://www.youtube.com/watch?v=ec_9rkWxrYA
Exponential Equations With Radicals: https://www.youtube.com/watch?v=d-E5isaIDTA
Difficult Exponential Equations: https://www.youtube.com/watch?v=F1b1beR3sNk
Exponential Equations - Fractions: https://www.youtube.com/watch?v=_iukwLh67xQ
Inverse of Logarithmic Functions: https://www.youtube.com/watch?v=hNsvGz7JPJQ
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Functions - Test Review: https://www.youtube.com/watch?v=1xATmTI-YY8
Algebra 1 Review Study Guide: https://www.youtube.com/watch?v=TbJ5gqLRpeM
Algebra Final Exam Review: https://www.youtube.com/watch?v=U0Y8nSmEpNM
Precalculus Final Exam Review: https://www.youtube.com/watch?v=Tj-V6KnwM5w
Full Length Exam Videos + Worksheets: https://bit.ly/4990rzU[+] Show More

Natural Logarithms

This algebra video tutorial provides a basic introduction into natural ...

Logarithms... How? (NancyPi)

MIT grad introduces logs and shows how to evaluate them. To skip ahead: 1) ...

MIT grad introduces logs and shows how to evaluate them. To skip ahead: 1) For how to understand and evaluate BASIC LOGS, skip to time 0:52. 2) For how to ...evaluate weirder logs, including the log of 0, 1, a FRACTION, or a NEGATIVE number, skip to time 6:44. 3) For NATURAL LOGS (LN X), skip to time 11:17. 4) For even weirder logs, including SOLVING for X and using the CHANGE-OF-BASE formula, skip to time 14:56. Nancy formerly of MathBFF explains the steps.

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1) BASIC LOGS: you can read log notation as "log, base 3, of 9 equals X". The small (subscript) number is called the base. You can always evaluate a log expression by rearranging it into something called exponential form. Every log expression is connected to an exponential expression. In this example, the log is connected to the exponential form "3 to the X power equals 9". This means, "3 raised to what power gives you 9?" Since 3 raised to the power of 2 equals 9, the answer for X is 2. This is also the answer for the value of the log expression. The log is always equal to the power (or exponent) in the exponential version, and in this case it equals 2. If you want, you can find the log value in your head just by asking yourself what power you need in order to turn the base number into the middle number ("argument" number). Note: if there is no base number in the log expression (no little subscript number), then the base is 10, since 10 is the default base.

2) WEIRDER LOGS (log of 0, 1, a negative number, or a fraction): you can use the same steps to rearrange log expressions that have a fraction, negative number, 0, or 1 in them. You can still rearrange them to be in exponential form just like you can with the basic logs from earlier. The log of 1 will always be 0, since 0 is the only power that can turn a base into 1. The log of 0 will always be undefined, since no power can turn a base into 0. The log of a negative number is undefined in the real number system, since no real power can turn a positive base into a negative number.

3) NATURAL LOGS (ln x): the natural log is just a special type of log where the base is e (the special math constant e, which is approximately 2.718 if you plug it into your calculator). You can use the same steps for rearranging the log expression into exponential form. Just remember that ln x means log, base e.

4) EVEN WEIRDER LOGS (solving for X, change-of-base formula): even if there is an X variable in the log part of an equation, you can still rearrange the equation into exponential form. This will let you solve for X. Sometimes you might need to use the change-of-base formula to evaluate a log expression. If there is no whole number power you know that works, it may actually be a decimal power that you can find by using the change-of-base formula. For example, you can re-write log, base 2, of 7 as (log 7)/(log 2) and use your calculator to find the decimal number if you need it.

For more of my math videos, check out: http://nancypi.com[+] Show More