<span>1) The differential equation that models the RC circuit is :
(d/dt)V_capacitor </span>+ (V_capacitor/RC) = (V_source/<span>RC)</span>
<span>Where the time constant of the circuit is defined by the product of R*C
Time constant = T = R*C = (</span>30.5 ohms) * (89.9-mf) = 2.742 s
2) C<span>harge of the capacitor 1.57 time constants
1.57*(2.742) = 4.3048 s
The solution of the differential equation is
</span>V_capac (t) = (V_capac(0) - V_capac(∞<span>))e ^(-t /T) + </span>V_capac(∞)
Since the capacitor is initially uncharged V_capac(0) = 0
And the maximun Voltage the capacitor will have in this configuration is the voltage of the battery V_capac(∞) = 9V
This means,
V_capac (t) = (-9V)e ^(-t /T) + 9V
The charge in a capacitor is defined as Q = C*V
Where C is the capacitance and V is the Voltage across
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /T) + 9V
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /2.742 s) + 9V
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /2.742 s) + 9V = -1.87V +9V
V_capac (4.3048 s) = 7.1275 V
Q (4.3048 s) = 89.9mF*(7.1275V) = 0.6407 C
3) The charge after a very long time refers to the maximum charge the capacitor will hold in this circuit. This occurs when the voltage accross its terminals is equal to the voltage of the battery = 9V
Q (∞) = 89.9mF*(9V) = 0.8091 C
Answer:
This is because when the pedal sprocket arms are in the horizontal position, it is perpendicular to the applied force, and the angle between the applied force and the pedal sprocket arms is 90⁰.
Also, when the pedal sprocket arms are in the vertical position, it is parallel to the applied force, and the angle between the applied force and the pedal sprocket arms is 0⁰.
Explanation:
τ = r×F×sinθ
where;
τ is the torque produced
r is the radius of the pedal sprocket arms
F is the applied force
θ is the angle between the applied force and the pedal sprocket arms
Maximum torque depends on the value of θ,
when the pedal sprocket arms are in the horizontal position, it is perpendicular to the applied force, and the angle between the applied force and the pedal sprocket arms is 90⁰.
τ = r×F×sin90⁰ = τ = r×F(1) = Fr (maximum value of torque)
Also, when the pedal sprocket arms are in the vertical position, it is parallel to the applied force, and the angle between the applied force and the pedal sprocket arms is 0⁰.
τ = r×F×sin0⁰ = τ = r×F(0) = 0 (torque is zero).
