Capacitance unit equivalence: select the correct statement for 1 microfarad (1 µF) Express the value relative to picofarads, millifarads, or farads.

Introduction / Context:Working across unit prefixes is routine in electronics. From tiny picofarad capacitors in RF circuits to microfarad electrolytics in power supplies, it is vital to translate quickly among pF, nF, µF, mF, and F. This question checks your fluency with SI prefixes for capacitance.

Given Data / Assumptions:

• 1 picofarad (pF) = 10^-12 farad.
• 1 microfarad (µF) = 10^-6 farad.
• 1 millifarad (mF) = 10^-3 farad.

Concept / Approach:Convert 1 µF into pF by dividing 10^-6 by 10^-12 to get 10^6 pF. Also compare with mF and F to reject incorrect equivalences. Always track exponents carefully and remember that “micro” is six orders of magnitude larger than “pico.”

Step-by-Step Solution:1) Start with 1 µF = 10^-6 F.2) Convert to pF: 10^-6 F / 10^-12 F per pF = 10^(−6 − (−12)) = 10^6 pF.3) Therefore, 1 µF equals 1,000,000 pF.4) Cross-check against mF: 1 mF = 10^-3 F, so 1000 mF = 1 F, not 1 µF.

Verification / Alternative check:Intermediate conversion: 1 µF = 1000 nF and 1 nF = 1000 pF. Multiplying 1000 * 1000 = 1,000,000 pF confirms the result.

Why Other Options Are Wrong:“1 millionth of a picofarad” equals 10^-6 pF = 10^-18 F, far smaller than 1 µF. “1000 millifarads” is 1 F, much larger. “1 million farads” is astronomically larger and unrealistic for standard components.

Common Pitfalls:Confusing milli (10^-3), micro (10^-6), nano (10^-9), and pico (10^-12). A quick mnemonic: m (−3) → µ (−6) → n (−9) → p (−12).

Final Answer:1 million picofarads