Many electronics devices can be dangerous even after they are shut off. Consider

Question

Many electronics devices can be dangerous even after they are shut off. Consider an RC circuit with a 140-?F-capacitor and a 1.50-M? resistor connected to a 210-V power source for a long time and then disconnected and shorted, as shown in the figure. How long will it be until the potential difference across the capacitor drops to below 51.5 V?

Many electronics devices can be dangerous even after they are shut off. Consider an RC circuit with a 140-?F-capacitor and a 1.50-M? resistor connected to a 210-V power source for a long time and then disconnected and shorted, as shown in the figure. How long will it be until the potential difference across the capacitor drops to below 51.5 V?

Explanation / Answer

voltage across capacitor =210 volt
time consatnt =RC=1.5*140=210
voltage at any time t is given by =210e^(-t/RC)
solving the equation , 51.5=210e^(-t/RC)
-t/RC=ln(51.5/210)=-1.405
so time t =1.405*210=295.16 sec

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