text: Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
  Share
  
  # Consider an Assembly of Three Conducting Concentric Spherical Shell of Radii A, B and Cas Shown in Figure Find the Capacitance of the Assembly Between the Points Aand B. - Physics
  
  ConceptCapacitors and Capacitance
  
  #### Question
  
  Consider an assembly of three conducting concentric spherical shell of radii a, b and c as shown in figure Find the capacitance of the assembly between the points Aand B.
  
  #### Solution
  
  The spherical shells form two spherical capacitors: one made by A and B and the other made by B and C.
  
  The capacitance of the spherical capacitor made by the shells of radii r1 and r2 is given by
  
  C = (4pi∈_0)/[[1/r_1 - 1/r^2]] = (4pi∈_0r_1r_2)/(r_2 - r_1)
  
  The capacitance of the capacitor made by A and B is given by
  
  C_(AB) = (4pi∈_0ab)/(b-a)
  
  The capacitance of the capacitor made by B and C is given by
  
  C_(BC) = (4pi∈_0bc)/(c-b)
  
  As the capacitors are in series, the net capacitance is given by
  
  1/C = 1/C_(AB) + 1/C_(BC)
  
  ⇒ C = (C_(AB)C_(BC))/(C_(AB)+C_(BC)) = (((4pi∈_0)^2 ab^2c)/((b-a)(c-b)))/((4pi∈_0ab)/((b-a))+(4pi∈_0bc)/((c-b))
  
  ⇒ C = ((4pi∈_0ab^2c)/((b-a)(c-b)))/(((ab(c-b)+bc(b-a))/((b-a)(c-b))))
  
  ⇒ C = (4pi∈_0ab^2c)/[[ab(c-b)+bc(b-a)]]
  
  ⇒ C = (4pi∈_0ab^2c)/(b^2(c-a)) = (4pi∈_0ac)/((c-a))
  
  Is there an error in this question or solution?
  
  #### Video TutorialsVIEW ALL [2]
  
  Solution Consider an Assembly of Three Conducting Concentric Spherical Shell of Radii A, B and Cas Shown in Figure Find the Capacitance of the Assembly Between the Points Aand B. Concept: Capacitors and Capacitance.
  S