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The charge q on the capacitor in a simple RLC circuit is
1
governed by the equation La" (!) + Ra'() + a 9() = E(), where L
is the inductance, R the resistance, C the capacitance, and E
the voltage source. Since the resistance of a resistor increases
with temperature, assume that the resistor is heated so that the
resistance at time t is R(t) = 2 + t92. If L = 0.1 H, C = 5 F, E(t)=0,
q(0) = 5 C, and q' (0) = 0 A, find the first four nonzero terms in a
power series expansion about t = 0 for the charge on the
capacitor.
0.1 henrys
000000
R(t)=2+t ohms
5 farads
q(0) = 5 coulombs
q'(0) = 0 amps
q(t)=
0.1 henrys The charge q on the capacitor in a simple RLC circuit is 1 governed by the equation Lq"(t) + Rq'(1) + 9() = E(t), where L is the inductance, R the resistance, C the capacitance, and E the voltage source. Since the resistance of a resistor increases with temperature, assume that the resistor is heated so that the resistance at time t is R(t)=2+12. If L=0.1 H, C=5 F. E(t)=0, 9(0)=5 C, and q' (O)=0 A, find the first four nonzero terms in a power series expansion about t=0 for the charge on the capacitor 5 farads 9(0)5 coulombs q'(0) = 0 amps R(t) = 2-t ohms ww 9(0)= (Type an expression that includes all terms up to order 4) To