A branch $AB$ of a circuit consists of a coil of inductance $2 \mathrm{~H}$ and a resistor of resist

Question

A branch $AB$ of a circuit consists of a coil of inductance $2 \mathrm{~H}$ and a resistor of resistance $4 \Omega$. A current of $3 \mathrm{~A}$ flows from $A$ to $B$ and is increasing at a rate of $2 \mathrm{~A/s}$. The potential difference $V_A - V_B$ is:

Professor PC Thomas Classes · Answer

(d) : Applying Kirchhoff's Voltage Law (KVL) from $A$ to $B$, tracing in the direction of the current: $V_A - iR - L \frac{di}{dt} = V_B$. We are given $i = 3 \mathrm{~A}$, $R = 4 \Omega$, $L = 2 \mathrm{~H}$, and the rate of increase of current $\frac{di}{dt} = 2 \mathrm{~A/s}$. Substituting the values: $V_A - (3 	imes 4) - (2 	imes 2) = V_B \Rightarrow V_A - 12 - 4 = V_B \Rightarrow V_A - V_B = 16 \mathrm{~V}$.