When a current source sits on the border between two meshes, you can’t write independent KVL equations for those meshes because the current through the shared edge is fixed by the source. The standard approach is to form a supermesh that goes around both meshes, skipping the current source, and write a single KVL around the outer boundary of that combined loop. Then introduce a constraint that ties the two mesh currents to the current source: the current through the shared edge equals the source value, so the difference between the two mesh currents equals that current, with the sign determined by the direction of the source. Solve the KVL for the supermesh alongside the current-relationship constraint to find the mesh currents. This is why forming a supermesh and using the current-source relation is the correct method. Replacing the current source with a Norton equivalent, solving the meshes independently, or ignoring the current source would not satisfy the fixed current constraint on the shared edge.

With a fixed supply voltage, the lamp’s wattage is determined by P = V^2 / R. If you increase the lamp’s resistance, the current it draws drops (I = V / R). Since power equals voltage times current, a smaller current means less power is dissipated. So the wattage decreases. It won’t stay the same or oscillate under a steady DC supply.

In a series circuit, the same current flows through every component. That current is I for the load, and Ohm’s law tells us the voltage across the load is V_load = I × R_load. Since the current is the same for that load, the voltage drop across it changes directly with the load’s resistance. If the resistance goes up, the voltage drop goes up in direct proportion; if the resistance goes down, the voltage drop goes down in direct proportion. So the voltage across the load and the resistance of that load are directly proportional. The other options don’t have this straightforward proportionality in a series circuit. The current through a load isn’t directly proportional to its own resistance because the overall circuit current depends on the total resistance and the source. While V = I R relates voltage, current, and resistance, the current varies with the circuit, so the pair that tracks changes together most directly is voltage across the load and its resistance. Wattage depends on both current and resistance (P = I^2 R), so it doesn’t line up with a simple direct proportionality to either quantity alone.

Emf is the energy per unit charge that a source provides to push charges around a circuit. The unit used for this potential difference is the volt, with 1 volt equaling 1 joule per coulomb (V = J/C). This tells you how strongly a source can drive current: a higher emf means more energy per charge available to move charges through the circuit. The other quantities describe different things: amperes measure how much charge flows per second (current), ohms measure resistance, and watts measure power. So the unit for electromotive force is volts.