Physics · Current Electricity
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Which of the following is the same unit as the farad?
- A
Ωs
- B
Ωs–1
- C
Ω–1s
- D
Ω–1 s–1
Farad is defined as charges held per unit of volt across the capacitor. Charges are current x time. So farad is the current x time over volt, or time over ohm.
This option is incorrect. The unit 'ohm second' (Ωs) represents resistance multiplied by time, which does not equate to capacitance. In electrical terms, this would instead relate to energy dissipation or other time-dependent resistance phenomena, not capacitance.
This option is incorrect. The unit 'ohm per second' (Ωs–1) represents resistance divided by time, which is not equivalent to capacitance. This unit does not align with the dimensional analysis required for capacitance.
This option is correct. The unit 'per ohm second' (Ω–1s) is indeed equivalent to the unit 'farad' (F), which is the SI unit of capacitance. It reflects the concept of conductance (the reciprocal of resistance) multiplied by time, which in dimensional terms aligns with capacitance.
This option is incorrect. The unit 'per ohm per second' (Ω–1 s–1) represents conductance per time, not capacitance. This unit is associated with a rate of change of conductance rather than the ability to store charge.
Tagged under Physics · Current Electricity · 2014