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Resistors dissipate energy in electric circuits, but their behavior is found time and again in diverse phenomena from the flux of biomass in bacterial cells to the flow of cars on city traffic grids.

Problem solving - Circuit elements


If a potential difference of \(V=115\text{ V}\) is applied across a capacitor arrangement with capacitances \(C_1=10\,\mu\text{F},\) \(C_2=6\,\mu\text{F}\) and \(C_3=15\,\mu\text{F},\) as shown in the above figure, what is the approximate stored energy \(U_3\) for capacitor 3?

A \(12.0\text{ V}\) battery is connected to a series of \(n\) capacitors, each of capacitance \(2\,\mu\text{F}.\) If the total stored energy is \(36.0\,\mu\text{J},\) what is \(n?\)

Approximately how much electrical energy is transferred to thermal energy in 3 hours by an electrical resistance of \(350.0 \,\Omega\) when the potential applied across it is \(90.0\text{ V}?\)

Consider a circuit where a potential difference of \(0.80 \text{ mV}\) is set up across a resistor with length \(2.50 \text{ cm}\) and radius \(1.30 \text{ mm}.\) Approximately how much charge drifts through the cross section of the resistor in \(30.00 \text{ s},\) assuming that the resistivity of the resistor is \(2.35 \times 10^{-8} \,\Omega\cdot\text{m}?\)

The above figure shows the electric potential \(V(x)\) along a copper wire as a function of position \(x.\) The radius of the copper wire is \(3.0\text{ mm}.\) If \(V_s=11.0\,\mu\text{V}\) and \(x_s=3.00\text{ m}\) in the figure, what is the approximate current in the wire?

The resistivity of copper is \(1.69 \times 10^{-8}\,\Omega\cdot\text{m}.\)


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