Kirchhoff’s Voltage Law (KVL) in a series loop: When all individual voltage drops and the source voltage are algebraically added around a closed series circuit, the total equals what value?

Introduction / Context:
This question targets Kirchhoff’s Voltage Law (KVL), a cornerstone of circuit analysis. KVL states that the algebraic sum of all potential rises and drops around any closed loop is zero. In other words, the supplied energy from sources is exactly balanced by the energy absorbed in passive elements, ensuring energy conservation in the loop.

Given Data / Assumptions:

• A single closed series loop.
• Ideal sources and components; steady-state DC for simplicity.
• Algebraic summation with proper sign convention (rises positive, drops negative, or vice versa).

Concept / Approach:
Traverse the loop in one direction and assign signs consistently: source voltage is a rise, component voltage drops are falls. By conservation of energy, total rises plus total drops must net to zero. This is independent of component values or current magnitude; it is a universal law for lumped-circuit models.

Step-by-Step Solution:

Verification / Alternative check:
Consider a numeric loop: a 12 V source feeding three series drops of 5 V, 4 V, and 3 V. Algebraic sum: +12 − 5 − 4 − 3 = 0, verifying KVL exactly.

Why Other Options Are Wrong:

• the total of the voltage drops / the source voltage: Each equals the other in magnitude, but the algebraic loop sum is zero.
• the total of the source voltage and the voltage drops: Misstates the law; their algebraic sum is not an arbitrary total but specifically zero.

Common Pitfalls:

• Ignoring sign convention and simply adding magnitudes.
• Confusing KVL (voltage) with KCL (current at nodes).

Final Answer:
zero