Physics

Physics

Problem

A battery of emf 24 V24\,\text{V} having negligible internal resistance is connected in series with three resistors R1=4 ΩR_1 = 4\,\Omega, R2=6 ΩR_2 = 6\,\Omega and R3=10 ΩR_3 = 10\,\Omega. a. (i) Derive an expression for the potential difference V2V_2 across the resistor R2R_2 in terms of the emf EE and the three resistances. b. (ii) Hence calculate the numerical value of V2V_2 for the given data. c. (iii) If the resistor R2R_2 is replaced by a variable resistor RxR_x, obtain an expression for RxR_x so that the potential difference across it equals 0.60E0.60E. Calculate RxR_x for the given values of R1R_1 and R3R_3. d. (iv) For the value of RxR_x obtained in part (iii), find the current delivered by the source and the power dissipated in RxR_x.
Intuitive explanation

This is a straightforward series circuit problem where the key insight is that current is the same everywhere in a series path. Find the total resistance by adding all three resistors, then use Ohm's law to find the current flowing through the circuit. Once you have the current, you can calculate the voltage drop across any individual resistor using V=IRV = IR.

Intuitive explanation

This is a straightforward series circuit problem where the key insight is that current is the same everywhere in a series path. Find the total resistance by adding all three resistors, then use Ohm's law to find the current flowing through the circuit. Once you have the current, you can calculate the voltage drop across any individual resistor using V=IRV = IR.

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