(a) Ohm's Law: At constant temperature, the current (I) flowing through a conductor is directly proportional to the potential difference (V) across its ends, i.e., V ∝ I, or V = IR.
For three resistors R₁, R₂, R₃ in parallel:
$$\frac{1}{R_P} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$
(b) From the diagram, one resistor R is in series with two resistors R connected in parallel.
Equivalent resistance of the two parallel resistors:
$$\frac{1}{R_P} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \implies R_P = \frac{R}{2}$$
Total resistance between X and Y (series combination):
$$R_{XY} = R + \frac{R}{2} = \frac{3R}{2}$$
$$\boxed{R_{XY} = \frac{3R}{2}}$$
Source: Chapter 11, Section 11.6 (Resistance of a System of Resistors)
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