E switch The figure above shows a circuit containing an electromotive force (a battery), a capacitor with a capacitance of C farads (F), and a resistor with a resistance of Rohms (). The voltage drop across the capacitor is Q/C, where is the charge (in coulombs), so in this case Kirchhoff's Law gives с RI+ Since the current is I = dQ dt R- = + = dQ dt 1 I E(t). we have Q = E(t). Suppose the resistance is 202, the capacitance is 0.05F, a battery gives a constant voltage of E(t) = 50V, and the initial charge is Q(0) = 0C. Find the charge and the current at time t. Q(t) I(t) =

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E
C
switch
The figure above shows a circuit containing an
electromotive force (a battery), a capacitor with a
capacitance of C farads (F), and a resistor with a
resistance of Rohms (). The voltage drop across the
capacitor is Q/C, where is the charge (in
coulombs), so in this case Kirchhoff's Law gives
RI+
Since the current is I
=
=
dQ
R +
dt
Q
=
dQ
dt'
1
E(t).
we have
Q = E(t).
Suppose the resistance is 202, the capacitance is
0.05F, a battery gives a constant voltage of
E(t) = 50V, and the initial charge is Q(0) = 0C.
Find the charge and the current at time t.
Q(t) =
I(t)
Transcribed Image Text:E C switch The figure above shows a circuit containing an electromotive force (a battery), a capacitor with a capacitance of C farads (F), and a resistor with a resistance of Rohms (). The voltage drop across the capacitor is Q/C, where is the charge (in coulombs), so in this case Kirchhoff's Law gives RI+ Since the current is I = = dQ R + dt Q = dQ dt' 1 E(t). we have Q = E(t). Suppose the resistance is 202, the capacitance is 0.05F, a battery gives a constant voltage of E(t) = 50V, and the initial charge is Q(0) = 0C. Find the charge and the current at time t. Q(t) = I(t)
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