State the basic electrical power relation between power, current, and voltage.

A \(12\,\mathrm{V}\) load draws \(3.0\,\mathrm{A}\). Find the power delivered to the load.

A \(4.0\,\Omega\) resistor carries \(2.0\,\mathrm{A}\). Find the power dissipated in the resistor.

A line with total resistance \(0.50\,\Omega\) carries \(10.0\,\mathrm{A}\). Find the line voltage drop and line power loss.

A \(2.0\,\mathrm{kW}\) load is delivered through a \(2.0\,\Omega\) line. Compare the line loss if the delivery voltage is \(100\,\mathrm{V}\) with the line loss if it is \(1000\,\mathrm{V}\).

A \(120\,\mathrm{V}\) source feeds a \(10.0\,\Omega\) load through total line resistance \(2.0\,\Omega\). Find the current, load power, line loss, and efficiency.

A battery has emf \(12.0\,\mathrm{V}\) and internal resistance \(0.50\,\Omega\). If it delivers \(4.0\,\mathrm{A}\), find the terminal voltage and load power.

A source has \(\mathcal E=24\,\mathrm{V}\) and internal resistance \(r=2.0\,\Omega\). It powers a \(6.0\,\Omega\) load. Find the current, load power, and efficiency.

For a source with \(\mathcal E=10\,\mathrm{V}\) and internal resistance \(r=5.0\,\Omega\), what load resistance gives maximum load power, and what is that maximum power?

Why is the maximum-power-transfer condition not the same as maximum efficiency for power distribution?

For fixed delivered power \(P\), delivery voltage \(V\), and line resistance \(R_{\mathrm{line}}\), derive the approximate scaling \(P_{\mathrm{loss}}=\frac{P^2R_{\mathrm{line}}}{V^2}\).

For the same delivered power and same line resistance, the delivery voltage is tripled. By what factor does the line loss change?

A system must deliver \(5.0\,\mathrm{kW}\) through a line with \(R_{\mathrm{line}}=1.0\,\Omega\). What delivery voltage is needed so line loss is no more than \(100\,\mathrm{W}\)? Use the approximate high-efficiency relation.

Two loads, \(60\,\Omega\) and \(30\,\Omega\), are connected in parallel across \(120\,\mathrm{V}\). Find the power in each load, the total power, and the total current.

A \(15\,\mathrm{A}\) fuse protects an ideal \(120\,\mathrm{V}\) circuit. What is the maximum ideal load power before the fuse rating is exceeded?

A conductor's resistance is halved, but the current through it is doubled. By what factor does the resistive power loss change?

For a source with emf \(\mathcal E\), internal resistance \(r\), and load resistance \(R_L\), derive \(P_L=\frac{\mathcal E^2R_L}{(r+R_L)^2}\).

Use the load-power expression \(P_L=\frac{\mathcal E^2R_L}{(r+R_L)^2}\) to show that maximum load power occurs when \(R_L=r\).

Explain why high-voltage transmission can reduce conductor size or heating for the same delivered power.

A \(48\,\mathrm{V}\) supply feeds a \(10.0\,\Omega\) load through two conductors, each with \(0.20\,\Omega\) resistance. Find the current, load voltage, line loss, and efficiency.