HelpContactFor teachers and institutes
>_StemPy Lab
Mock TestsClasses

>_StemPy Lab

Learn. Solve. Code the solutions. Test yourself.

Live examsFree mock exams, timed and rankedEveryone starts together, and your score and rank come the moment it ends.See the exams →

Learn

  • Physics
  • Chemistry
  • Mathematics
  • Biology
  • Python Programming
  • Statistics & Data Science
  • Classes
  • Groups

Practice

  • Problems
  • Quizzes
  • Mock Tests
  • Prepare for an Exam
  • Question Sets
  • Exams
  • Certificates
  • Python Labs
  • AI Practice Generator
  • Student-Created Tests

Community

  • Discussions
  • Resources
  • Notes
  • Blog

Account

  • Log in
© 2026 senLearn. All rights reserved.HelpAboutContactPrivacy PolicyTerms of UseRefund Policy
  1. Problems
  2. /A 5.0 µF capacitor rated 150 V is joined in series with a 20 µF capacitor rated 400 V…
MediumPhysicsHigh School (11–12)Electricity & Magnetism › Electric Potential and CapacitanceNumericalpythonAPA-LevelIBAEEE (Amrita)AMUEEEAP EAPCET
+17 more exams
BCECECOMEDK UGETCUET UGGUJCETJCECEJKCETKCETKEAMKIITEELPUNESTMET (Manipal)MHT-CETOJEESRMJEEETS EAPCET

A 5.0 µF capacitor rated 150 V is joined in series with a 20 µF capacitor rated 400 V…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A 5.0 μF5.0\ \mu\text{F}5.0 μF capacitor rated 150 V150\ \text{V}150 V is joined in series with a 20 μF20\ \mu\text{F}20 μF capacitor rated 400 V400\ \text{V}400 V. What is the equivalent capacitance? What is the greatest charge the pair can hold? What is the greatest voltage that can safely be put across the pair?

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

μF
μC
V
Need a reminder? The key ideaShowHide

In parallel the voltage is shared and the capacitances add: C=C1+C2+…C = C_1 + C_2 + \dotsC=C1​+C2​+… In series the charge is shared and 1C=1C1+1C2+…\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dotsC1​=C1​1​+C2​1​+… For two capacitors in series, V1=V C2C1+C2V_1 = V\,\dfrac{C_2}{C_1 + C_2}V1​=VC1​+C2​C2​​. In a series chain, the capacitor that reaches its rating first sets the limit.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. The equivalent. C=5.0 μF×20 μF5.0 μF+20 μF=4.0 μFC = \dfrac{5.0\ \mu\text{F} \times 20\ \mu\text{F}}{5.0\ \mu\text{F} + 20\ \mu\text{F}} = 4.0\ \mu\text{F}C=5.0 μF+20 μF5.0 μF×20 μF​=4.0 μF.

Step 2. The charge limits. The 5.0 μF5.0\ \mu\text{F}5.0 μF capacitor reaches 150 V150\ \text{V}150 V at 5.0 μF×150 V=750 μC5.0\ \mu\text{F} \times 150\ \text{V} = 750\ \mu\text{C}5.0 μF×150 V=750 μC. The 20 μF20\ \mu\text{F}20 μF capacitor reaches 400 V400\ \text{V}400 V at 20 μF×400 V=8000 μC20\ \mu\text{F} \times 400\ \text{V} = 8000\ \mu\text{C}20 μF×400 V=8000 μC.

Step 3. The smaller one wins. The pair can hold 750 μC750\ \mu\text{C}750 μC at most.

Step 4. The voltages. The 5.0 μF5.0\ \mu\text{F}5.0 μF capacitor has 150 V150\ \text{V}150 V. The 20 μF20\ \mu\text{F}20 μF capacitor has 750 μC20 μF=37.5 V\dfrac{750\ \mu\text{C}}{20\ \mu\text{F}} = 37.5\ \text{V}20 μF750 μC​=37.5 V. Together, 150 V+37.5 V=187.5 V150\ \text{V} + 37.5\ \text{V} = 187.5\ \text{V}150 V+37.5 V=187.5 V.

Check. 750 μC4.0 μF=187.5 V\dfrac{750\ \mu\text{C}}{4.0\ \mu\text{F}} = 187.5\ \text{V}4.0 μF750 μC​=187.5 V.

Watch out. The sum of the ratings, 550 V550\ \text{V}550 V, is far too high. The 20 μF20\ \mu\text{F}20 μF capacitor is used at only a small part of its rating.

Log in to save this for later
← All Problems
← An 18 µF capacitor is joined in series with a parallel pair of 3.0 µF and 6.0 µF…Twelve identical capacitors, each 8.0 µF and rated 50 V, are made into 3 strings in parallel… →
More onElectricity & Magnetism › Electric Potential and Capacitance

Discussion (0)

Log in to join the discussion.

Loading…

Learn it in

  1. Capacitors in series and parallelCombining Capacitors and Stored Energy

More on this topic

  1. An 8.0 µF air capacitor is charged to 50 V…Hard
  2. A 24 V battery charges a 250 µF capacitor through a 100 Ω resistor until the capacitor is full…Medium
  3. A 12 µF capacitor is charged to 100 V. An 8.0 µF capacitor is charged to 50 V…Medium
  4. The plates of an air capacitor have an area of 0.050 m² and are 2.0 mm apart…
UPESEAT
VITEEE
Hard
  • A 3.0 µF capacitor and a 6.0 µF capacitor are first joined in parallel across a 60 V battery…Medium
  • All problems on this topic →

    Want to go further in Electricity & Magnetism › Electric Potential and Capacitance?

    With Standard, you also open 11 more problems, 2 Python labs and 1 extra course. Everything you have used here stays free, always.

    Part of our upcoming paid plans.