Use the following scenario for the next two problems Capacitors C_1 and C_2 have
ID: 1413767 • Letter: U
Question
Use the following scenario for the next two problems Capacitors C_1 and C_2 have identical geometries except C_2 has a dielecric material in the entire capacitor gap. The dielectric constant of the material is 2.5. The equivalent capacitance of the combination of C_1 and C_2 is 4.5 times 10^-11 F. Initially uncharged. C_1 and C_2 are connected in parallel with a battery with a terminal voltage of 1.5 V. What is the capacitance of C_1? 1.3 times 10^-11 2.3 times 10^-11 F 3.2 times 10^-11 F 6.3 times 10^-11 F 1.6 times 10^-10 F Which of the following expression about the potential difference across C_1(V_1) and that across C_2(V_2) correct? V_1 + V_2 = 1.5 V V_1 = 2.5 V_2 2.5V_1 = V_2 V_1 = V_2 = 1.5 V Multiple choices above are correct.Explanation / Answer
C1+C2 =4.5 * 10^-11 F
since C2 has dielectric and area and distance between the plates are same as C1 then C2 = k C1 = 2.5 C1
C1 + 2.5 C1 = 4.5 * 10^-11 F
C1 = 4.5 * 10^-11/ 3.5 = 1.3 * 10^-11 F
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when the capacitor s are connceted in parallel the potential difference acrosss the capacitors are same
so V1 = V2 = 1.5 V
option (D) is correct ansswer