As a capacitor discharges through a resistor, the voltage across the resistor is

Question

As a capacitor discharges through a resistor, the voltage across the resistor is a maximum at the beginning of the process near the middle of the process at the end of the process after one time constant When a capacitor discharges through a resistor, the current in the circuit is a minimum at the beginning of the process near the middle of the process at the end of the process after one time constant Another way to describe the discharge time of an Rc circuit is to use a time interval called the half-life, which is defined as the time for the capacitor to lose half its initial charge. Is the time constant longer or shorter than the half-life? Explain your reasoning. Does charging a capacitor in an RC circuit to 25% its maximum value take longer or shorter than one time constant? Explain. A capacitor and a resistor are connected through a switch to an emf. At the instant just after the switch is closed. the current in the circuit is zero. the voltage across the capacitor is the same as the emf. the voltage across the resistor is zero. the voltage across the resistor is the same as the emf. Both a and c are true.

Explanation / Answer

1.

the Voltage across the resistor is maximum at the begining since current in the circuit is maximum in the begining .

and from ohm's law

, V = i R

hence V is maximum when "i" is maximum

2)

the current in the circuit is propotional to exponent of time . hence the current is minimum near the end of the process

3)

during discharging , time constant is defined as the time in which charge on the capacitor decreases to 36.8% of its maximum value .

hence time constant is shorter than the half life

4)

during charging , time constant is defined as the time in which charge on the capacitor increases to 63.2% of its maximum value .

hence to charge to 25% of maximum value takes less time than the time constant

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