Loop Rule — Prelims Questions

In the circuit shown, if $I_1 = 2,\text{A}$ and $I_2 = 1,\text{A}$, what is the potential difference across the $4,Omega$ resistor?

A circuit contains a $10,\text{V}$ battery and a $5,Omega$ resistor. If we traverse the resistor in the direction of current flow, and then traverse the battery from its positive to negative terminal, what is the algebraic sum of potential changes according to KVL?

Consider a loop in a circuit with a $6,\text{V}$ battery (traversed from negative to positive), followed by a $3,Omega$ resistor (current $I$ flowing in traversal direction), and then a $9,\text{V}$ battery (traversed from positive to negative). If the KVL equation for this loop is $6 - 3I - 9 = 0$, what is the value of current $I$?

Which of the following statements about Kirchhoff's Loop Rule is INCORRECT?

In a circuit, a current $I$ flows through a $R_1 = 2,Omega$ resistor and then through a $R_2 = 3,Omega$ resistor, both in series. If a $15,\text{V}$ battery is connected across this series combination, and a loop is traced from the negative terminal of the battery, through $R_1$, then $R_2$, and back to the positive terminal of the battery, what is the KVL equation?

Two batteries with EMFs $E_1 = 10,\text{V}$ and $E_2 = 5,\text{V}$ are connected in series with a resistor $R = 5,Omega$. $E_1$ and $E_2$ are connected such that their positive terminals are facing each other. If current $I$ flows clockwise in the loop, what is the KVL equation if we traverse the loop clockwise starting from the negative terminal of $E_1$?