Question

A ​270-kilo-ohm ​[k​] resistor and a ​.3 microfarad ​[​F] capacitor rated at 240 volts​ [V] are connected in​ series, meaning that all of the current through the resistor enters the capacitor.

Assuming that the capacitor is initially fully discharged and that a constant voltage of 5 volts​ [V] is maintained across the​ resistor, how​ long, in units of seconds​ [s], can this circuit operate before the voltage rating of the capacitor is​ exceeded?

Answer 1

The circuit can operate for approximately 405 seconds before the voltage rating of the capacitor is exceeded.

Step-by-step explanation:

To determine how long the circuit can operate before the voltage rating of the capacitor is exceeded, we need to calculate the time it takes for the capacitor to reach its maximum voltage. The time constant (RC) can be calculated using the values of the resistance (270 kilo-ohm) and the capacitance (.3 microfarad).

RC = 270 kilo-ohm * .3 microfarad = 270 * 10^3 * .3 * 10^-6 = 81 seconds.

The time it takes for the capacitor to reach its maximum voltage, or to be fully charged, is approximately 5 time constants. Therefore, the circuit can operate for approximately 405 seconds (81 seconds * 5) before the voltage rating of the capacitor is exceeded.