A student writes the integral equation _ 0 ^ t [I_1(t)+I_2(t)+I_3(t) ]
PHYSICS · Single correct · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits
Problem
A student writes the integral equation
∫0Δt[I1(t)+I2(t)+I3(t)]dt=0
for three time-dependent currents meeting at a node, where positive values represent currents directed toward the node. Which statement best evaluates whether this time-integrated form is necessary in addition to the instantaneous statement of charge conservation at the node?
(a) The equation is required only when the currents vary with time; the instantaneous condition applies solely to steady currents.
(b) The equation is redundant because the instantaneous condition already guarantees that no net charge accumulates, so integrating merely restates the same principle.
(c) The equation is incorrect because currents cannot be meaningfully integrated over time to obtain charge.
(d) The equation is valid only if Δt is infinitesimally small; for any finite Δt a net charge can accumulate at the node.