A 20 μF capacitor at 6.0 V discharges through 50 kΩ. Sketch labelled Q–t and V–t graphs. On a third set of axes sketch I–t for current defined positive into the initially positive plate, then show how it changes if positive current is defined out of that plate. Mark initial values and values at one time constant; explain the Q–t gradient and I_out–t area.

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τ = 1.0 s; Q₀ = 120 μC, V₀ = 6.0 V, I_in,0 = −0.120 mA. At τ: 44.1 μC, 2.21 V, −0.0441 mA. Opposite reference reverses I sign. τ = (50 × 10³)(20 × 10⁻⁶) = 1.0 s; Q₀ = CV₀ = 120 μC. Draw smooth exponential Q and V curves towards zero with labelled axes, starting at 120 μC and 6.0 V. At τ, Q = 120/e = 44.1 μC and V = 6.0/e = 2.21 V. I_in starts at −V₀/R = −0.120 mA and rises towards zero from below; at τ it is −0.0441 mA. I_out is the reflected curve above the time axis, representing the same discharge in the opposite current convention. The Q–t gradient is I_in; the area under I_out–t is charge discharged, reaching 120 μC for a complete discharge.

Sketch discharge and defend the current sign

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