Two capacitors are identical except that they have different insulators in the gap between the conductors. Capacitor A has an air filled gap while capacitor B uses a material with dielectric constant 3 to keep the conductors apart. The two capacitors are connected in series. What is true of the voltage V across the capacitors, the charge Q on the capacitors, and the electric field E in the gap of the capacitors?

Question

Physics

Ingram

17 November, 11:37

Two capacitors are identical except that they have different insulators in the gap between the conductors. Capacitor A has an air filled gap while capacitor B uses a material with dielectric constant 3 to keep the conductors apart. The two capacitors are connected in series. What is true of the voltage V across the capacitors, the charge Q on the capacitors, and the electric field E in the gap of the capacitors?

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Gabrielle Monroe · Answer 1

Answer: V1=Q/C and V2=Q / (3*C); Q1=Q2=Q; E2=E1/3

Explanation: In order to explain this problem mwe have to consider the expression for a capacitor given by:

C=Q/V also we have to take into account the capacitor with dielectric constant equal to 3.

As the capacitors are identical abd considering that they are connected in series, the total voltage is equal:

V=V1+V2 = (Q1/C1) + (Q2/V2); Q1=Q2=Q due to are connected in serie.

V = (Q/C1) + (Q/V2) = Q * ((1/C1) + 1/C2)

besides we also know that C2=3*C1 then we have:

V2=Q/3*C1 so V2=V1/3

Finally, the electric field for each capacitor is given by:

E1=V1/d where d is the separation between the plates

E2=V2/d as we know that V2=V1/3

E2=V1/3*d

then E2=E1/3