Answer:
a, 1.775s
b, 17.04μC
c, 1.28s
Explanation:
Given
R = 1.25MΩ
C = 1.42µF
ε = 12.0 V
q = 8.78 µC
Time constant, τ = RC
τ = (1.25*10^6) * ( 1.42*10^-6)
τ = 1.775s
q• = εC
q• = 12 * 1.42*10^-6
q• = 17.04*10^-6C
q• = 17.04μC
Time t =
q = q• [1 - e^(t/τ)]
t = τIn[q•/(q•-q)]
t = 1.775In[17.04μC/(17.04μC-8.78μC)]
t = 1.775In(2.06)
t = 1.775*0.723
t = 1.28s
Given values,
(a)
The time constant will be:
→ [tex]\tau = RC[/tex]
[tex]= (1.25\times 10^6)\times (1.42\times 10^{-6})[/tex]
[tex]= 1.77 \ s[/tex]
(b)
The maximum charge will be:
→ [tex]q = \varepsilon C[/tex]
[tex]= 12\times 1.42\times 10^{-6}[/tex]
[tex]= 17.04 \ \mu C[/tex]
(c)
The time taken will be:
→ [tex]t = \tau \ ln[\frac{q \cdot}{q \cdot - q} ][/tex]
By putting the values,
[tex]= 1.775 \ ln[\frac{17.04}{17.04-8.78} ][/tex]
[tex]= 1.775 \ ln(2.06)[/tex]
[tex]= 1.775\times 0.723[/tex]
[tex]= 1.28 \ s[/tex]
Thus the responses above are correct.
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