If C1=14micro farad C2=20micro farad C3=micro farad and insulated plate of C1 be a potential of 100V while one plate of C3 being earthed. What is the P.D between the plates of C2 when the three capacitors are connected in series? Correct answer is 24.4micro farad.?

Question

Answer

What's the value of C₃ ?

Answer

Calculating the equivalent capacitance:

Capacitors in series add reciprocally: 1/Ceq = 1/C1 + 1/C2 + 1/C3

Substituting values: 1/Ceq = 1/14 + 1/20 + 1/x

Where x is the unknown capacitance of C3

Using a common denominator: 1/Ceq = (20x + 14x + 280)/(280x)

Simplifying: Ceq = (280x)/(34x + 280)

Finding the charge on each capacitor:

Charge is the product of capacitance and voltage: Q = CV

For C1: Q1 = 14 x 10^-6 x 100 = 1.4 x 10^-3 C

For C2: Q2 = Ceq x V

Using V = Q1 / (C1 + C3): Q2 = (280x)/(34x + 280) x (1.4 x 10^-3 / (14 x 10^-6 + x))

Calculating the potential difference:

Potential difference is the difference in voltage between the plates of a capacitor

For C2: V2 = Q2 / C2

Substituting values: V2 = [(280x)/(34x + 280)] x (1.4 x 10^-3 / 20 x 10^-6)

Simplifying: V2 = 7 x (280x)/(34x + 280)

Solving for x:

Substituting V2 = 24.4 x 10^3 V (given): 24.4 x 10^3 = 7 x (280x)/(34x + 280)

Cross-multiplying and simplifying: 34x = 19.6

Therefore, x = 0.58 micro farad

Thus, the capacitance of C3 is 0.58 micro farad and the potential difference between the plates of C2 is 24.4 volts.

Similar Class 12 Doubts

Two identical parallel plate capacitors are connected in series and then joined with a battery of 100V. A sheet of dielectric constant 4 is inserted between the plates of second capacitor.?

Two capacitors of capacitances 5 micro farad and 10 micro farad are charged to 16 volts and 10 volts respectively. Find the common potential when they are connected in parallel?

N identical capacitors are joined in series give an effective capacitance of C units . What will be the capacitance if yhe capacitor are now connected in parallel combination?

Top Courses for Class 12

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams