 Solution

ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2014/9/ii/solution

A = V / (4 R)

, and the homogeneous equation has decay rate

2 R / L

. Imposing

I_{1} (0) = 0

gives

I_{1} (t) = \frac{V}{4 R} (1 - e^{- t / τ}), A = \frac{V}{4 R}, τ = \frac{L}{2 R} .

As a separate check, the Thévenin equivalent seen by

L

V /2

and resistance

R + (2 R ∥ 2 R) = 2 R

, again giving

τ = L / (2 R)

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