Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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# Two Capacitors of Capacitance 20⋅0 Pf and 50⋅0 Pf Are Connected in Series with a 6⋅00 V Battery. Find (A) the Potential Difference Across Each Capacitor and (B) the Energy Stored in Each Capacitor. - Physics

ConceptElectric Potential Difference

#### Question

Two capacitors of capacitance 20⋅0 pF and 50⋅0 pF are connected in series with a 6⋅00 V battery. Find (a) the potential difference across each capacitor and (b) the energy stored in each capacitor.

#### Solution

Given :

C_1 = 20.0  "pF"

C_2 = 50.0  "pF"

When the capacitors are connected in series, their equivalent capacitance is given by C_(eq) = (C_1C_2)/(C_1+C_2)

∴ Equivalent capacitance,C_(eq) = ((50 xx 10^-12) xx (20 xx 10^-12))/((50 xx 10^-12)+(20 xx 10^-12)) = 1.428 xx 10^-11  "F"

(a) The charge on both capacitors is equal as they are connected in series. It is given by

q = C_(eq) xx V

⇒ q = (1.428 xx 10^-11) xx 6.0  "C"

Now ,

V_1 = q/C_1 = ((1.428 xx 10^-11) xx 6.0  "C")/((20 xx 10^-12))

⇒ V_1 = 4.29  "V"

and

V_2 = (6.00 - 4.29) V = 1.71   "V"

(b) The energies in the capacitors are given by

E_1 = q^2/(2C_1)

= [(1.428 xx 10^-11) xx 6.0]^2 xx 1/(2 xx 20 xx 10^-12)

= 184  "pJ"

and

E_2 = q^2/(2C_1)

= [(1.428 xx 10^-11) xx 6.0]^2 xx 1/(2 xx 50 xx 10^-12)

= 73.5  "pJ"

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Solution Two Capacitors of Capacitance 20⋅0 Pf and 50⋅0 Pf Are Connected in Series with a 6⋅00 V Battery. Find (A) the Potential Difference Across Each Capacitor and (B) the Energy Stored in Each Capacitor. Concept: Electric Potential Difference.
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