A 6.44 E+06 ohm resistor and a 1.00 microfarad capacitor are connected in a single loop circuit with a seat of emf of E = 2.00 V. At 6.00 s. after the connection is made, what is the rate at which energy (in joules/second) is being delivered by the seat of emf?
R = 6.44*10^6 Ohms.
C = 1.00 uF = 1*10^-6 Farads.
n=t/R*C=6 / (6.44*10^6 * 1*10^-6)=0.932
Vc = E-Vr.
Vr = E/e^n. = 2/e^0.932 = 0.788 Volts.
I=V/R = 0.788/6.44*10^6=1.22*10^-7 Amps
Energy=E*I*T=(2*1.22*10^-7)*6=1.47*10^-6
Joules.
Correction:
Energy=E*I=2 * 1.22*10^-7=2.45*10^-7 Watts = 2.45*10^-7 Joules/s.
To find the rate at which energy is being delivered by the seat of emf, we first need to calculate the current flowing through the circuit using Ohm's Law. The formula for current is I = V/R, where I is the current, V is the voltage, and R is the resistance.
Given:
Resistance (R): 6.44 E+06 ohms
Voltage (E): 2.00 V
We can substitute these values into the formula to find the current:
I = 2.00 V / 6.44 E+06 ohms
Since the resistance is given in scientific notation, we will need to convert it to a decimal number. 6.44 E+06 is equivalent to 6.44 * 10^6 ohms.
I = 2.00 V / 6.44 * 10^6 ohms
I = 0.310 V / 10^6 ohms (simplifying)
So, the current flowing through the circuit is 0.310 A (or 310 mA).
Now, with the current value, we can calculate the rate at which energy is being delivered by the seat of the emf. The formula for power (rate of energy) is P = IV, where P is power, I is current, and V is voltage.
Given:
Current (I): 0.310 A
Voltage (E): 2.00 V
We can substitute these values into the formula to find the power:
P = 0.310 A * 2.00 V
P = 0.620 W
Therefore, the rate at which energy is being delivered by the seat of emf is 0.620 joules per second (or 0.620 watts).