Question #291430

A 1000mf capacitor is charged to 10v and 16uf capacitor is charged to 400v.these are then connected in parallel with plates carrying similar charges connected together. Determined the total stored energy before and after joining them. Is final energy the same as the initial energy?

1
Expert's answer
2022-02-01T09:54:38-0500

Energy stored in capacitor

E=½CV2E= ½CV^2


Energy before connection =12×1000×103×102+12×16×106×4002=\frac{1}{2}×1000×10^{-3}×10^2+\frac{1}{2}×16×10^{-6}×400^2


=51.28J=51.28J


After connection

CT=C1+C2C_T=C_1+C_2

Total capacitance=1000×103+16×106=1000×10^{-3}+16×10^{-6}

=1.000016=1.000016

Charge on capacitor

Q=CVQ=CV

Total charge

=1000×103×10+16×106×400=1000×10^{-3}×10+16×10^{-6}×400

=10.0064=10.0064



E=½CV2E=½CV^2


But V=QVV=\frac {Q}V


E=Q22CE=\frac{Q^2}{2C}

Energy after connection

=12×10.006421.000016=\frac{1}{2}×\frac{10.0064^2}{1.000016}

=50.0632=50.0632


Energy is not conserved

Some of if is converted into heat in the connecting wires.



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