In a parallel circuit, power P = V²/R. Since both resistors have the same voltage, the thermal energy ratio is inversely proportional to resistance. Thus, E100Ω : E 200Ω = 200 : 100 = 2:1. Answer: (b) 2:1.

Using the formula for parallel battery circuits: V = 12/1 + 13/2 /1/1 + 1/2 = 12 + 6.5/1.5 = 11.67V Thus, the answer is (a) 11.6 V to 11.7 V.

Let the emfs be E₁ and E₂. From the potentiometer principle: E₁ + E₂/E₁ – E₂ = 50/10 = 5 Solving, E₁/E₂ = 5/1. Answer: (d) 5:1.

Using P = V²R/(R+r)² , equating power for R = 4Ω and R = 1Ω, solving gives r = 2Ω and E = 12V. Maximum power = 18W. Answer: (c).

The current is given by I = dQ/dt = a – 2bt. It starts at, reaches a maximum at t = 0 and decreases linearly with time. Thus, the correct answer is (a) decreases linearly with time.