The charge flowing through a resistance R varies with time t as Q = a

1.	The charge flowing through a resistance R varies with time t as Q = at - bt2. The total heat produced in R is(a) a3R/6b(b) a3R/3b(c) a3R/2b(d) a3R/b
Answer» Correct Answer is:(a) a³R/6b Q = at - bt². i = dQ dt = a - 2bt. i = 0 for t = t₀ = a/ 2b, i.e., current flow from t = 0 to t = t₀. The heat produced = i²R dt. for t ∈ [0, t₀]

The charge flowing through a resistance R varies with time t as Q = at - bt2. The total heat produced in R is(a) a3R/6b(b) a3R/3b(c) a3R/2b(d) a3R/b

Answer»

Correct Answer is:(a) a³R/6b

Q = at - bt².

i = dQ dt = a - 2bt.

i = 0 for t = t₀ = a/ 2b, i.e., current flow from t = 0 to t = t₀.

The heat produced = i²R dt. for t ∈ [0, t₀]