Electric current and DC circuits

A wire carries a constant current of $0.80\mathrm{A}$ for $5.0$ minutes. Compute the charge that crosses a section of the wire and the corresponding number of electrons.

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An aluminum cable with a cross section of $2.5\mathrm{m}{\mathrm{m}}^2$ carries a current of $10\mathrm{A}$. Aluminum has $1.8\cdot 10^{29}$ conduction electrons per cubic meter. Compute the current density and the drift velocity of the electrons.

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A copper wire, with resistivity $1.7\cdot 10^{-8}\Omega \cdot \mathrm{m}$ and diameter $0.50\mathrm{mm}$, has resistance $1.7\Omega$. Compute the length of the wire.

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A copper winding, with temperature coefficient $3.9\cdot 10^{-3}{\mathrm{K}}^{-1}$, has resistance $50.0\Omega$ at $20{}^{\circ }\mathrm{C}$. While a motor is running its resistance becomes $57.8\Omega$. Compute the temperature of the winding.

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An ideal source with $\mathcal{E}=24\mathrm{V}$ supplies a $4.0\Omega$ resistor in series with the parallel combination of two resistors of $6.0\Omega$ and $12\Omega$. Compute the equivalent resistance, the current delivered and the current in the $12\Omega$ resistor.

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A $2.2\mathrm{kW}$ electric heater operates at $230\mathrm{V}$ for $3.0$ hours. Compute the current drawn, the resistance of the heater and the energy consumed, in kilowatt-hours and in joules.

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Two resistors, $R_1=10\Omega$ and $R_2=20\Omega$, are connected to an ideal source with $\mathcal{E}=30\mathrm{V}$, first in series and then in parallel. In both cases compute the power dissipated in each resistor.

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A battery with electromotive force $12\mathrm{V}$ and internal resistance $0.40\Omega$ supplies a $5.6\Omega$ resistor. Compute the current, the terminal voltage and the power dissipated inside the battery.

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A source has electromotive force $6.0\mathrm{V}$ and, with its terminals connected by a wire of negligible resistance, delivers $3.0\mathrm{A}$. Compute the internal resistance, the load resistance that receives the maximum power and the value of that power.

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An ideal source with ${\mathcal{E}}_1=9.0\mathrm{V}$ in series with $R_1=1.0\Omega$ and an ideal source with ${\mathcal{E}}_2=3.0\mathrm{V}$ in series with $R_2=2.0\Omega$ are connected between the nodes $A$ and $B$ with the positive terminals toward $A$; $R_3=4.0\Omega$ is connected between the same nodes. Compute the currents in the three branches, with their directions.

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In a Wheatstone bridge the resistor $R_1=120\Omega$ connects the node $A$ to the node $C$, the resistor $R_2=360\Omega$ connects $C$ to the node $B$, the resistor $R_3=50\Omega$ connects $A$ to the node $D$ and the unknown resistor $R_x$ connects $D$ to $B$. The source is connected between $A$ and $B$, and a galvanometer connected between $C$ and $D$ carries no current. Compute $R_x$.

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An uncharged $10\mu \mathrm{F}$ capacitor is charged through a $47\mathrm{k\Omega }$ resistor by an ideal source with $\mathcal{E}=10\mathrm{V}$. Compute the time constant and the time after which the voltage across the capacitor is $6.0\mathrm{V}$.

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A $470\mu \mathrm{F}$ capacitor, charged to a voltage of $20\mathrm{V}$, discharges through a $1.0\mathrm{k\Omega }$ resistor. Compute the initial current, the voltage across the capacitor after $1.0\mathrm{s}$ and the total energy dissipated in the resistor.

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