Power In Electric Circuits

- When equal resistors each of resistance are connected in series, total resistance is: which is the maximum resistance. - When connected in parallel, total resistance is: which is the minimum resistance. Therefore, the ratio is: Note: The ratio is , so correct answer should be (D).

The sensitivity of a potentiometer is directly related to the potential gradient along its wire, which is defined as the voltage drop per unit length of the potentiometer wire. Mathematically, the potential gradient is given by: where is the voltage across the wire and is the length of the wire. When the current through the potentiometer wire is increased, the voltage drop across the wire increases proportionally, resulting in a higher potential gradient . A higher potential gradient means that even a small change in the length of the wire corresponds to a larger change in voltage, which improves the precision and accuracy of measurements. Therefore, increasing the current through the potentiometer wire increases the potential gradient and thereby increases the sensitivity of the potentiometer.

Kirchhoff’s second law, also known as the loop rule, states that the algebraic sum of all electromotive forces (emfs) and potential differences (voltage drops) around any closed loop in an electrical circuit is zero. Mathematically, this can be expressed as: where represents the emfs and represents the potential drops across circuit elements. This law is a direct consequence of the conservation of energy principle, implying that as a charge moves around a complete loop, the net energy gained must equal the net energy lost. Thus, the total energy supplied by sources in the loop is completely used up by the resistive elements and other components.

Power , voltage , and resistance are related by: For the two bulbs: Therefore, the ratio of resistances: But since corresponds to the 40 W bulb and to 60 W bulb, ratio . Note: This matches option (D), so correct answer is (D) .

Electrical conductivity is defined as the reciprocal of resistance : Given the resistance: we calculate the conductivity as: This means the material has a conductivity of (since is equivalent to siemens), indicating how easily electric current can flow through it.