Electric Circuits

What fundamental principle underlies Kirchhoff's Junction Rule?

In a circuit, two wires meet at a junction. If 3A of current enters the junction through one wire and 1A leaves through the other, what is the current in the third wire connected to the junction?

At a junction, if $I_1 = 5\text{A}$ (entering) and $I_2 = 2\text{A}$ (leaving), what is $I_3$ if it is leaving the junction?

At a junction in a circuit, the following currents are observed: $I_1 = 6\text{A}$ (entering), $I_2 = 2\text{A}$ (leaving), $I_3 = 3\text{A}$ (entering), and $I_4$ is unknown. What is the magnitude and direction of $I_4$?

Four wires are connected at a junction. The currents in three of the wires are: 4A entering, 2A leaving, and 5A entering. What is the current in the fourth wire?

A junction has four branches. $I_1$ (entering) is 3A, $I_2$ (entering) is 4A, $I_3$ (leaving) is 2A. Determine $I_4$ (leaving).

A circuit contains a junction with three resistors connected to it. The voltage source in the circuit provides 12V. Two of the resistors have currents of 1A entering and 0.5A leaving the junction, respectively. If the third resistor has a resistance of 10 ohms, what is the current through it, and is it entering or leav...

In a complex circuit, a junction connects a 3\Omega resistor, a 6\Omega resistor, and an unknown resistor $R$. The current through the 3\Omega resistor is 2A entering the junction, and the current through the 6\Omega resistor is 1A leaving the junction. If the voltage across resistor $R$ is 6V, what is the current thro...

A circuit has a junction with three branches. The current $I_1$ entering the junction is dependent on a voltage source $V$ such that $I_1 = V/2$. The current $I_2$ leaving the junction is 2A. If $V = 8\text{V}$, what is the current $I_3$ (leaving)?

According to Kirchhoff's Junction Rule, what sign convention is typically used for currents entering a junction?