Kirchhoff's Laws — Prelims Questions

In the given circuit, if $I_1 = 3\,\text{A}$ and $I_2 = 2\,\text{A}$, what is the value of current $I_3$?

A circuit loop consists of a 12 V battery, a $4\,\Omega$ resistor, and a $2\,\Omega$ resistor connected in series. If the current flowing in the loop is $I$, what is the correct KVL equation if traversed in the direction of current, starting from the negative terminal of the battery?

Consider a circuit with two loops. If there are 4 nodes and 6 branches, how many independent KCL and KVL equations are required to solve the circuit?

Which of the following statements is INCORRECT regarding Kirchhoff's Laws?

In the circuit shown, find the current $I_1$ using Kirchhoff's Laws. (Assume a circuit with two loops: Loop 1 with a 10V battery, $R_1=2\,\Omega$, $R_2=3\,\Omega$. Loop 2 with a 5V battery, $R_2=3\,\Omega$, $R_3=1\,\Omega$. $R_2$ is common to both loops. Let $I_1$ be current in Loop 1, $I_2$ in Loop 2, and $I_3$ be current through $R_2$ downwards. Assume $I_1$ flows clockwise in Loop 1, $I_2$ flows clockwise in Loop 2.)

In a circuit, if a current of $4\,\text{A}$ enters a junction and then splits into two branches carrying currents $I_A$ and $I_B$. If $I_A = 1.5\,\text{A}$, what is the value of $I_B$?

A loop in a circuit contains a voltage source of $6\,\text{V}$ and two resistors of $R_1 = 1\,\Omega$ and $R_2 = 2\,\Omega$. If the current flows from the positive terminal of the battery, through $R_1$, then $R_2$, and back to the negative terminal, what is the potential difference across $R_2$?