AP Physics C: E&M:: Electric Circuits

What is KIRCHHOFF'S VOLTAGE LAW (also called the LOOP RULE), and what does it state about the SUM of voltage changes around any CLOSED LOOP in a circuit?

- **A)** Kirchhoff's Voltage Law states that the SUM of all voltage changes (gains and drops) around any COMPLETE, CLOSED loop in a circuit must equal ZERO -- this is a direct consequence of energy conservation, since a charge returning to its starting point must have net zero change in potential energy
- **B)** Kirchhoff's Voltage Law states that voltage changes around a closed loop always sum to a LARGE, NONZERO value, contradicting the actual energy-conservation basis of this law
- **C)** This law has no actual relationship between voltage changes around a closed loop and energy conservation
- **D)** Kirchhoff's Voltage Law applies only to loops containing EXACTLY ONE resistor, with no actual applicability to more complex multi-component loops

What is KIRCHHOFF'S CURRENT LAW (the JUNCTION RULE, already introduced in the earlier DC Circuits unit), and why is it ESSENTIAL for analyzing MULTI-LOOP circuits with multiple junctions?

- **A)** Kirchhoff's Current Law states that the total current ENTERING a junction must equal the total current LEAVING it (a consequence of charge conservation); for multi-loop circuits with several junctions, this rule provides ADDITIONAL equations needed (alongside the loop rule) to solve for all the unknown currents in each branch
- **B)** Kirchhoff's Current Law states that current entering a junction is always GREATER than current leaving it, implying charge accumulates at junctions
- **C)** Kirchhoff's Current Law is only useful for SINGLE-LOOP circuits, with no actual additional value for analyzing multi-loop circuits
- **D)** This law has no actual relationship to solving for unknown currents in multi-loop circuits with multiple junctions

For a MULTI-LOOP circuit with MULTIPLE unknown branch currents, what GENERAL STRATEGY combines Kirchhoff's Current Law (junction rule) and Kirchhoff's Voltage Law (loop rule) to solve for all the unknowns?

- **A)** Only the loop rule is needed to solve a multi-loop circuit, with the junction rule providing no additional useful information
- **B)** This concept has no actual relationship between combining the junction rule and loop rule to solve multi-loop circuit problems
- **C)** Only the junction rule is needed to solve a multi-loop circuit, with the loop rule providing no additional useful information
- **D)** Apply the JUNCTION RULE at each distinct junction (current in = current out) and the LOOP RULE around each independent closed loop (sum of voltage changes = 0), generating a SYSTEM of equations that can be solved SIMULTANEOUSLY for all the unknown branch currents

When a BATTERY is traversed in a circuit loop from its NEGATIVE terminal to its POSITIVE terminal (in the direction of traversal), what SIGN convention applies to this voltage change when applying Kirchhoff's Voltage Law?

- **A)** Traversing a battery from negative to positive always represents a voltage DECREASE (a negative contribution), the reverse of the actual sign convention
- **B)** Traversing a battery from its NEGATIVE to POSITIVE terminal represents a voltage INCREASE (a positive contribution, +EMF) in the loop equation -- consistent with moving toward the terminal at higher potential
- **C)** The sign convention for traversing a battery is always ZERO, regardless of which direction the loop is traversed
- **D)** This concept has no actual relationship between traversal direction through a battery and the resulting sign convention in Kirchhoff's Voltage Law

When a RESISTOR is traversed in a circuit loop IN THE SAME DIRECTION as the assumed CURRENT flowing through it, what SIGN convention applies to this voltage change when applying Kirchhoff's Voltage Law?

- **A)** The sign convention for traversing a resistor depends only on the resistor's resistance value, with no actual dependence on the direction of traversal relative to current
- **B)** This concept has no actual relationship between traversal direction through a resistor and the resulting sign convention in Kirchhoff's Voltage Law
- **C)** Traversing a resistor in the SAME direction as the assumed current represents a voltage DECREASE (a negative contribution, -IR) in the loop equation -- consistent with current flowing from higher to lower potential through a resistor
- **D)** Traversing a resistor in the same direction as current always represents a voltage INCREASE, the reverse of the actual sign convention

What is a CAPACITOR's behavior in a DC circuit IMMEDIATELY after a switch is closed (at t=0, when the capacitor is initially UNCHARGED), specifically regarding the CURRENT that flows through the circuit at that first instant?

- **A)** Capacitor behavior in a DC circuit has no actual distinction between the moment right after the switch closes and the eventual steady-state behavior
- **B)** Immediately after the switch closes (t=0), an initially uncharged capacitor behaves like a 'SHORT CIRCUIT' (effectively zero resistance) -- the CURRENT is at its MAXIMUM value at this first instant, since the capacitor offers no initial opposition to charge flowing onto its plates
- **C)** This concept has no actual relationship between a capacitor's initial charge state and the circuit's current immediately after a switch closes
- **D)** Immediately after the switch closes, an uncharged capacitor behaves like an 'OPEN CIRCUIT' (infinite resistance), with ZERO current flowing at t=0 -- the reverse of the actual initial behavior

What is a CAPACITOR's behavior in a DC circuit AFTER A LONG TIME has passed (at STEADY STATE, when the capacitor is FULLY CHARGED), specifically regarding the CURRENT that flows through the branch containing that capacitor?

- **A)** Current through a capacitor's branch remains constant and unchanged from t=0 all the way to steady state, with no actual transition in behavior
- **B)** This concept has no actual relationship between a capacitor's steady-state charge and the resulting current through its branch
- **C)** After a long time (steady state), a FULLY CHARGED capacitor behaves like an 'OPEN CIRCUIT' (effectively infinite resistance) -- the CURRENT through the capacitor's branch drops to ZERO, since the capacitor can no longer accept additional charge once fully charged to the applied voltage
- **D)** After a long time, a fully charged capacitor behaves like a 'SHORT CIRCUIT' (zero resistance), with MAXIMUM current continuing to flow through its branch -- the reverse of the actual steady-state behavior

What is an RC CIRCUIT, and what is the mathematical FORMULA for the TIME CONSTANT (tau) of an RC circuit, in terms of the resistance and capacitance values?

- **A)** This concept has no actual mathematical relationship between an RC circuit's time constant and its resistance or capacitance values
- **B)** The time constant is calculated as tau = R/C (resistance divided by capacitance), rather than multiplied by capacitance
- **C)** An RC circuit contains a resistor and a capacitor together; the time constant is tau = R*C (resistance multiplied by capacitance), measured in SECONDS -- this characteristic time scale determines how QUICKLY the capacitor charges or discharges
- **D)** The time constant depends only on capacitance, with no actual relationship to the circuit's resistance