If W amount of work is required to increase t | vedclass

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Question

(D) The work done $W$ to change the potential of a capacitor from $V_1$ to $V_2$ is given by the change in stored energy: $W = U_f - U_i = \frac{1}{2}

Vedclass · Accepted Answer

$1.67$

Vedclass · Answer

(D) The work done $W$ to change the potential of a capacitor from $V_1$ to $V_2$ is given by the change in stored energy: $W = U_f - U_i = \frac{1}{2} C (V_2^2 - V_1^2)$.For the first case,$W = \frac{1}{2} C (10^2 - 5^2) = \frac{1}{2} C (100 - 25) = \frac{1}{2} C (75) = 37.5 C$.For the second case,$W' = \frac{1}{2} C (15^2 - 10^2) = \frac{1}{2} C (225 - 100) = \frac{1}{2} C (125) = 62.5 C$.Taking the ratio: $\frac{W'}{W} = \frac{62.5 C}{37.5 C} = \frac{62.5}{37.5} = \frac{625}{375} = \frac{5}{3} \approx 1.67$.Therefore,$W' = 1.67\ W$.

If $W$ amount of work is required to increase the voltage of a capacitor from $5\ V$ to $10\ V$,how much work is required to increase the voltage from $10\ V$ to $15\ V$ (in $W$)?

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