Final answer:
The statement is false; voltage drops can occur across open switches due to their high resistance, and the power dissipated is small due to the large resistance value or small voltage across a closed switch.
Step-by-step explanation:
The statement that a voltage drop never occurs across a switch is false. There is a voltage drop across an open switch because the switch, when open, acts like a very high resistance and thus the entire voltage of the voltage source appears across it. However, when a switch is closed, it has nearly zero resistance and, therefore, the voltage drop is almost zero. The power dissipated by an open switch is very small since power P is given by P = V^2/R, and the resistance R is extremely large, leading to a small power value. Conversely, for a closed switch, the power dissipation is small because the voltage drop V is very small.
Regarding circuit diagrams, the statement that the voltage is the same at every point in a given wire is false. According to the principles of circuit theory, voltage drops do occur across components like resistors, and the voltage at different points in a wire can indeed vary, especially if there are components with impedance or resistance between those points.
The voltage drop across resistors in parallel is the same, but the current through each can be different due to their potential differences and respective resistances.