A capacitor is discharging through a resistor. It takes a time ‘T’ for the charg

Question

A capacitor is discharging through a resistor. It takes a time ‘T’ for the charge to decrease to one half of its original value. It takes a time ‘t’ for the stored energy to decrease to onehalf of its original value. How is ‘t’ related to ‘T’?

a) T = 4t

b) T = 2t

c) T = t

d) T = (1/2)t

e) T = (1/4)t

f) Need more information.

Explain your response in the space provided.

1) Conceptual Question Limit answer to space provided below A capacitor is discharging through a resistor. It takes a time 'T' for the charge to decrease to one half of its original value. It takes a time 't' for the stored energy to decrease to one half of its original value. How is't, related to T? d) T (1/2)t. e) T= (1/4t. f) Need more information. a) T = 4t. b) T= 2t. c) T = t. Explain your response in the space provided

Explanation / Answer

prerequisite

Energy stored in capacitor = Q2 /2C  

discarging equation of capacitor Q= Qi e-t/RC

where Q = charge on capacitor and C = capacitance

so energy to be half ====> Q should be Q/sqrt(2)

now question became t = time when charge reduces to Q/sqrt(2)

and T = time when charge reduces to Q/2

Q/sqrt(2) = Q e-t/RC so t = 1/2 RC ln2  

and Q/2 = Q e-T/RC so T= RC ln2

t= 1/2 T so T = 2t

ans - B

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