The quantity t1/2=τ ln 2 is called the half-life of an exponential decay, where τ=rc is the time constant in an rc circuit. the current in a discharging rc circuit drops by half whenever t increases by t1/2. for a circuit with "r=1.0 kω and c=4.0 μf, if the current is 6.0 ma at t=4.0 ms", at what time (in ms) will the current be 3.0 ma?

6.77 ms

Explanation:

τ=RC

= 1 x 10³ x 4 x 10⁻⁶

4 X 10⁻³

t1/2=τ ln 2

= 4 X 10⁻³ X ln 2

= 2.77 x 10⁻³

2.77 ms

Half life = 2.77 ms

Current is 6 mA AT t = 4 ms

and half life is 2.77 ms ie current becomes half after every 2.77 ms

so current will reduce from 6 mA to 3 mA in further  2.77 ms

or at t = 4 + 2.77 = 6.77 ms current will become 3 mA.

5 w for 1hr = 5x60x60 joules=300x60=3000x6=18,000j as total energy conversion. efficiency of bulb needed for radiant to thermal within 18000

nah.   i'm just sleepy.