What current condition defines resistors connected in series?

What voltage condition defines resistors connected in parallel?

Find the equivalent resistance of \(4.0\,\Omega\), \(6.0\,\Omega\), and \(10.0\,\Omega\) connected in series.

Find the equivalent resistance of \(6.0\,\Omega\) and \(3.0\,\Omega\) connected in parallel.

A \(12\,\mathrm{V}\) battery is connected to \(3.0\,\Omega\) and \(5.0\,\Omega\) resistors in series. Find the current and the voltage across each resistor.

A \(20\,\mathrm{V}\) source is connected to \(2.0\,\Omega\), \(3.0\,\Omega\), and \(5.0\,\Omega\) resistors in series. Find the voltage across the \(5.0\,\Omega\) resistor.

A \(4.0\,\Omega\) resistor and a \(6.0\,\Omega\) resistor are connected in parallel across \(12\,\mathrm{V}\). Find each branch current and the total current.

A \(4.0\,\Omega\) resistor is in series with a parallel group made from \(6.0\,\Omega\) and \(3.0\,\Omega\). The network is connected to \(12\,\mathrm{V}\). Find the total equivalent resistance and the source current.

A resistor dissipates \(18\,\mathrm{W}\) when the current through it is \(3.0\,\mathrm{A}\). Find the resistance and the voltage across it.

Two resistors, \(2.0\,\Omega\) and \(8.0\,\Omega\), carry the same current. Which resistor dissipates more power, and by what factor?

Two resistors, \(2.0\,\Omega\) and \(8.0\,\Omega\), are connected across the same voltage. Which resistor dissipates more power, and by what factor?

What happens to the equivalent resistance of a parallel network when another finite positive resistor is added in parallel? Explain from the reciprocal rule.

Derive the series-resistor rule \(R_{\mathrm{eq}}=R_1+R_2+\cdots\) from Ohm's law and the voltage sum.

Derive the parallel-resistor rule \(\frac{1}{R_{\mathrm{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots\) from Ohm's law and current conservation.

A voltage divider has \(R_1\) from the source node to the output node and \(R_2\) from the output node to ground. Derive \(V_{\mathrm{out}}\) in terms of the source voltage \(V\).

A total current \(I\) enters two parallel resistors \(R_1\) and \(R_2\). Derive the current through \(R_1\).

What resistor must be placed in parallel with \(12\,\Omega\) to make an equivalent resistance of \(4.0\,\Omega\)?

A divider has \(9.0\,\Omega\) on top and \(3.0\,\Omega\) on bottom across \(12\,\mathrm{V}\). First find the unloaded output across the bottom resistor. Then connect a \(3.0\,\Omega\) load in parallel with the bottom resistor and find the loaded output.

A total current of \(5.0\,\mathrm{A}\) enters two parallel branches, \(8.0\,\Omega\) and \(12.0\,\Omega\). Use current division to find the current through the \(8.0\,\Omega\) branch.

A complicated resistor network is replaced by \(R_{\mathrm{eq}}\) at the same two terminals. What exactly must be unchanged for every applied terminal voltage, and what internal information can be lost by the replacement?