Question

A capacitor of value 4 uF charged at 50V is connected with another capacitor of value 2uF charged at100V. in such a way that plates of similar charges are connected together. Before joining and afterjoining the total energy in multiples 10^-2J will be:​

Answer 1

Answer:

ans. Uinitial=1.5×10^-2Joules

Ufinal=1.3×10^-2Joules

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Answer 2

Answer:

Before joining and after joining the total energy in multiples 10^-2J will be 1.5 and 1.33 Joules respectively.

Explanation:

Total energy before joining:

$U_b=\frac{1}{2}C_1V_1^2+ \frac{1}{2}C_2V_2^2$         (1)

From the question we have,

C₁=4μF=4×10⁻⁶F

V₁=50volt

C₂=2μF=2×10⁻⁶F

V₂=100

Inserting values in equation (1) we get;

$U_b=\frac{1}{2}\times 4\times 10^-^6\times 50^2+ \frac{1}{2}\times 2\times 10^-^6\times 100^2$

$U_b=1.5\times 10^-^2\ J$     (2)

Total energy after joining:

$U_a=\frac{1}{2}CV^2$        (3)

C=equivalent capacitance

V=common potential

C=4×10⁻⁶+2×10⁻⁶=6×10⁻⁶F

$V=\frac{C_1V_1+C_2V_2}{C_1+C_2}$      (4)

Placing the required values in equation (4) we get;

$V=\frac{4\times 10^-^6\times 50+2\times 10^-^6\times 100}{4\times 10^-^6+2\times 10^-^6}$

$V=66.67volt$      (6)

Inserting the values in equation (3) we get;

$U_a=\frac{1}{2}\times 6\times 10^-^6\times (66.67)^2$

$U_a=1.33\times 10^-^2\ J$     (3)

Before joining and after joining the total energy in multiples 10^-2J will be 1.5 and 1.33 Joules respectively.

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