Concept:Resistance in series:When resistors are connected end-to-end in a circuit, they are said to be in "series."R = R1 + R2 + R3....Current remains the same across all the resistors connected in series. Resistance in parallel: When both ends of resistors are connected, they are said to be in parallel. 1/R = 1/R1 + 1/R2 = 1/R3 ....The potential difference across all the resistors connected in parallel remains the same. Electric Power:The energy consumed per unit of time or the rate of doing work is called power. Power = work done / time taken = Vq / t = VI = V2/R = I2RCalculation: Resistors A (r ?), B (2r ?), and C (3r ?) are connected in parallel.Equivalent resistance, 1/R1 = 1/r + 1/2r +1/3r = 6+3+2/ 6r = 11/6 r R1= 6r/11Now, the resistors R1, D, F, and G are in series.R2 = 6r/11 + r + 2r + 3r = (6r + 11r + 22r + 33r) / 11 = 72r / 11Equivalent current, I in the circuit = V/R2 = \(\frac{11E}{72r}\)Potential difference across C, V' = IR1 = \(\frac{11E}{72r}\) À” \(\frac{6r}{11}\) = E / 12PG = I2G = \((\frac{11E}{72r})^2\) À” 3r = \(\frac{121E^2 À” 3r}{72r À”72r}\) = 121E2/ 72r À” 24r (since current remains same in series combination)PC = V' 2/C = \(\frac{(\frac{E}{12})^2}{3r}\) = E2/ 12 À” 12 À” 3r (since voltage remains same in parallel combination)PC/ PG = \(\frac{\frac{E^2}{12 À” 12 À” 3r}}{\frac{121 E^2}{72r À” 24}}\) = \(\frac{E^2 À” 72r À” 24}{12 À” 12À” 3r À” 121 E^2}\) = 4/ 121The ratio (PC/PG) = 4/121.