A 47 micro farad capacitor is placed in series with a resistor. If the capacitor is to charge up to 50% of its maximum charge in 1 second, how big of a resistor do we want?
Someone Please Help Me with this problem
Someone Please Help Me with this problem
-
voltage on a cap, charging
v = v₀[1–e^(–t/τ)]
R is resistance in ohms,
C is capacitance in farads
t is time in seconds
RC = τ = time constant
v = v₀[1–e^(–t/τ)]
0.5 = [1–e^(–t/τ)]
e^(–t/τ) = 0.5
–t/τ = ln 0.5 = -0.693
–1/τ = -0.693
τ = 1.44 sec = RC
R = 1.44 / 47µ = 30700 ohms
.
v = v₀[1–e^(–t/τ)]
R is resistance in ohms,
C is capacitance in farads
t is time in seconds
RC = τ = time constant
v = v₀[1–e^(–t/τ)]
0.5 = [1–e^(–t/τ)]
e^(–t/τ) = 0.5
–t/τ = ln 0.5 = -0.693
–1/τ = -0.693
τ = 1.44 sec = RC
R = 1.44 / 47µ = 30700 ohms
.
-
okay