Question: Suppose an RC-series circuit has a variable resistor. If the resistance at time t is defined by R(t) = k 1 + k 2 t,

Suppose an RC-series circuit has a variable resistor. If the resistance at time t is defined by R(t) = k₁ + k₂t, where k₁ and k₂ are known positive constants, then the differential equation in (9) of Section 3.1 becomes

(k₁ + k₂t) dq/dt + 1/C q = E(t),

where C is a constant. If E(t) = E₀ and q(0) = q₀, where E₀ and q₀ are constants, then show that

q(t) = E₀C + (q₀ - E₀C) [k₁/(k₁ + k₂t)]^1/Ck2.

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