An initially uncharged capacitor is being charged by a constant current source. If the charging time is extended by 5 s , the energy stored in the capacitor increases by 125 % . The original charging time is

Step-by-step solution

For a capacitor charged by a constant current I , the charge at time t is Q = It . The energy stored in the capacitor is U = Q^2 2C = I^2 t^2 2C . This shows that U t^2 . Let the initial charging time be t₀ and the initial energy be U₀ . When the time is extended by 5 s , the new time is t' = t₀ + 5 . The new energy is U' = U₀ + 1.25 U₀ = 2.25 U₀ . Since U t^2 , we have U' U₀ = ( t' t₀ )^2 . 2.25 = ( t₀ + 5 t₀ )^2 Taking the square root of both sides: 1.5 = t₀ + 5 t₀ 1.5 t₀ = t₀ + 5 0.5 t₀ = 5 t₀ = 10 s . Answer: 1