What is Decibel?

The human ear has logarithmic characteristics i.e. the loudness of sound is proportional to log of power which causes it.

Suppose a certain sound power 'P' produces a loudness 'L'. Now let loudness be increased to 'mL' by increasing power to 'kP'.(k, m are constants)

If loudness is again increased by same amount i.e 2mL, it is found that power required is K^2 * P.

If process is repeated 'N' times then

Pn = K^N * P  ---> log(Pn / P) =N*logK

N = [log(Pn/P)] / log K

taking natural log of above equation we get
N = K*log(Pn/P)

but napiers logs are difficult to work.

taking logs to base 10 we arrive at

N = 10 * log10(Pn/P) 

where 'Pn' is power derived and 'P' is power absorbed. 

The unit of above equation is decibel.



Checking capacitors with an ohmmeter

Set the range of Ohm meter to higher range greater than 1MOhm. The ohm-meter leads are to be connected across leads of capacitor. Fora good capacitor, the meter first shows low value and then slowly recedes to a higher value. The reading gets stabilized to  a higher value after some time due to charging action.

For ceramic, paper and Mica capacitors, the resistance falls in the range 500 - 1000 MOhm.
For electrolytic capacitors, it is around 1MOhm.

If ohmmeter reading immediately goes to zero and stays there, the capacitor is short circuited.

If capacitor shows no charging action but just reads very high resistance it may be open.

Stray capacitance:

The wiring and components in a circuit have capacitance to metal chassis. The stray capacitance is typically 5 to 10PF.  

Leakage resistance of capacitor: 

Consider a capacitor charged by a DC voltage source. If the source is removed a perfect capacitor would keep its charge indefinitely.