A condenser with a safe working voltage of 250 volts DC is most likely to break down if used across which type of line?

A condenser, or capacitor, with a safe working voltage of 250 volts DC is designed to handle direct current at that specified voltage. When considering its application in an AC circuit, it's essential to recognize the peak voltage that an AC line can produce.

In the case of a 250 volt 60 Cycle AC line, the root mean square (RMS) voltage of 250 volts will lead to a peak voltage of about 353 volts (calculated as RMS voltage multiplied by the square root of 2). Since this peak voltage exceeds the capacitor's rated working voltage of 250 volts, the condenser is likely to break down when subjected to this AC line due to over-voltage conditions during the peak cycles.

By contrast, a 120 volt AC line has a peak voltage of approximately 170 volts, which is safe for the condenser. A 400 volt 50 Cycle AC line has a peak voltage of about 565 volts, which far exceeds the condenser's working voltage, making it also unsuitable, but since the 250 volt AC line's peak voltage reaches this dangerous threshold straight away, this situation is the most immediate risk. Lastly, a low voltage DC line would generally not exceed the condenser's rated voltage, making it a safer