(i) Rank the following five capacitors from greatest to smallest capacitance, no

Question

(i) Rank the following five capacitors from greatest to smallest capacitance, noting any cases of equality. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)
(a) a 20-µF capacitor with a 4-V potential difference between its plates
(b) a 30-µF capacitor with charges of magnitude 90 µC on each plate
(c) a capacitor with charges of magnitude 80 µC on its plates, differing by 2 V in potential
(d) a 10-µF capacitor storing energy 125 µJ
(e) a capacitor storing energy 250 µJ with a 10-V potential difference


(ii) Rank the same capacitors in part (i) from largest to smallest according to the potential difference between the plates.


(iii) Rank the capacitors in part (i) in the order of the magnitudes of the charges on their plates.


(iv) Rank the capacitors in part (i) in the order of the energy they store.

Explanation / Answer

Ca = 20 units, Va= 4 units, Qa = 80 units , Ea = 160 units = QV/2
Cb = 30 units, Vb = 90/30 = 3 units, Qb = 90 units , Eb = 135 units = QV/2
Cc= 80/2 = 40 units, Vc = 2 units, Qc = 80 units , Ec = 80 units = QV/2
Cd= 10 units, Vd = 5 units, Qd = 50 units , Ed = 125 units = QV/2
Ce = 5 units ( because 1/2 Ce * 10*10 = 250), Ve = 10 units, Qe = 50 units , Ee = 125 units = QV/2

f) Q*v/2 = 360 => QV = 720 units
=> V = 720/120 = 6 units
=> Cf = 20 units, Vf = 6 units, Qf = 120 units , Ef = 360 units = QV/2
1)Cc > Cb > Ca=Cf > Cd>Ce

2) Ve > Vf> Vf > Va> Vb> Vc

3) Qf > Qb > Qa= Qc > Qd =Qe

4) Ef> Ea> Eb> Ee=Ed>Ec

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