In the circuit shown charge q varies with time t as q = t² - 5, where q is in coulomb and t is in second. At time t = 3 second, voltage VAB in volt will be (a) 8 (b) 12 (c) 14 (d) 18

Answer: (c). ABI = 6 Aq/C = 1 VL dI/dt = 1 VIR = 12 V At t = 3 s: q = 9 - 5 = 4 C, I = dq/dt = 2t = 6 A, dI/dt = 2 A/s Current flows from A to B (it charges the + plate). Drops along A to B: Capacitor q/C = 4/4 = 1 V, inductor LdI/dt = 0.5 × 2 = 1 V, resistor IR = 6 × 2 = 12 V VAB = 1 + 1 + 12 = 14 V So the answer is (c) 14.

In the circuit shown charge q varies with time t as q = t² - 5, where… | MHT CET 2026 (20 Apr, Shift 1)

Q1MHT CET 2026 · 20 APR · SHIFT 1Medium

Electric Current, Drift Velocity & Current Density

In the circuit shown charge q varies with time t as $q = t^{2} - 5$ , where q is in coulomb and t is in second. At time $t = 3$ second, voltage $V_{AB}$ in volt will be

Show answer and solution

Answer: (c)

At $t = 3\text{ s}$ : $q = 9 - 5 = 4\text{ C}$ , $I = \dfrac{dq}{dt} = 2t = 6\text{ A}$ , $\dfrac{dI}{dt} = 2\text{ A/s}$
Current flows from A to B (it charges the + plate). Drops along A to B:
Capacitor $\dfrac{q}{C} = \dfrac{4}{4} = 1\text{ V}$ , inductor $L\dfrac{dI}{dt} = 0.5 \times 2 = 1\text{ V}$ , resistor $IR = 6 \times 2 = 12\text{ V}$
$V_{AB} = 1 + 1 + 12 = 14\text{ V}$
So the answer is (c) 14.

Report a mistake

Electric Current, Drift Velocity & Current Density question from MHT CET 2026 (20 Apr, Shift 1)

More questions on Electric Current, Drift Velocity & Current Density