A heating coil is used to boil a specific amount of water. When connected to a pure DC voltage source V₀ , it takes 15 minutes to boil the water. If the source is replaced by a mixed voltage source given by V(t) = V₀ + V₀ ( t) , the time taken to boil the same amount of water under identical conditions will be

Step-by-step solution

Let the resistance of the heating coil be R and the heat required to boil the water be H . When connected to the pure DC source V₀ , the power dissipated is P_ dc = V₀^2 R . The heat produced in time t₁ = 15 minutes is: H = V₀^2 R t₁ When connected to the mixed voltage source V(t) = V₀ + V₀ ( t) , the effective (RMS) voltage squared is: V_ rms ^2 = (V₀ + V₀ ( t))^2 V_ rms ^2 = V₀^2 + V₀^2 2 = 3 2 V₀^2 The new power dissipated is P_ mixed = V_ rms ^2 R = 1.5 V₀^2 R . The heat produced in time t₂ must be the same: H