Consider the expression of time period:
` T=1/f `
` T=1/{100kHz} `
` T=0.01ms `
As Pulse width is half of period.
Pulse width ` ={T}/2 `
Pulse width ` ={0.01ms}/2 `
Pulse width ` =0.005ms~~5\mus `
Also the time constant of the given circuit is:
` tau=R_{eqv}C `
` tau={R+R_s}C `
` tau={50\Omega+R}\times 1nF `
Here the time constant, pulse width and time period is obtained.
The value of resistor R so that the time constant of this RC circuit is less than 1/10 of the pulse width is obtained as follows:
` \text{Pulse width}-{1/10}\text{Pulse width}=tau `
` 5\mus-{1/10}\times 5mus={50\Omega+R}\times 1nF `
` {9/10}\times 5\times 10^{-6}s={50\Omega+R}\times 1\times 10^{-9}F `
` 45={50\Omega+R}times 10^{-2} `
` 4500={50\Omega+R} `
` R=(4500-50)Omega `
` R=4450\Omega `
Here the value of resistor R so that the time constant of this RC circuit is less than 1/10 of the pulse width is obtained.
Therefore the value of resistor R so that the time constant of this RC circuit is less than 1/10 of the pulse width is obtained as 4450ohms.