A storage battery has an emf of 6.3 volts and an internal resistance of 0.01 ohm. it is to be charged for 120 amperes.hours from a 30 volt emf source having a resistance of 0.08 ohm at the rate of 20 amperes.
a. compute for the resistance needed
b. what is the cost of electrical energy used in charging the battery if electricity cost 12.50 Pesos per kilowatt.hour
To solve this problem, we will use the principles of electrical circuits and power calculations.
a. To compute the resistance needed, we can use Ohm's Law. The formula for calculating resistance is:
Resistance (R) = (Source voltage (V) - Battery voltage (V)) / Charging current (I)
In this case, the source voltage (V) is 30 volts, the battery voltage (V) is 6.3 volts, and the charging current (I) is 20 amperes. Plugging in these values into the formula, we have:
R = (30 V - 6.3 V) / 20 A
R = 23.7 V / 20 A
R = 1.185 ohms
Therefore, the resistance needed to charge the battery at the rate of 20 amperes is approximately 1.185 ohms.
b. To calculate the cost of electrical energy used in charging the battery, we need to determine the amount of energy consumed. The formula for calculating electrical energy is:
Energy (E) = Power (P) x Time (t)
We know that power is equal to voltage multiplied by current. In this case, the power (P) is equal to the product of the source voltage (30 volts) and the charging current (20 amperes):
P = 30 V x 20 A
P = 600 watts
Now we need to determine the time (t). The time is given as 120 amperes-hours. We can convert this to hours by dividing by the charging current:
t = 120 A.hr / 20 A
t = 6 hours
Therefore, the energy consumed (E) is:
E = 600 watts x 6 hours
E = 3600 watt-hours
Since 1 kilowatt-hour (kWh) is equal to 1000 watt-hours, we need to convert the energy consumed to kilowatt-hours:
E = 3600 watt-hours / 1000
E = 3.6 kWh
Finally, to calculate the cost of electrical energy used, we multiply the energy consumed (in kilowatt-hours) by the cost per kilowatt-hour (12.50 Pesos):
Cost = 3.6 kWh x 12.50 Pesos/kWh
Cost = 45.00 Pesos
Therefore, the cost of electrical energy used in charging the battery is 45.00 Pesos.
a. To compute the resistance needed, we can use Ohm's Law. The formula is:
Resistance (R) = (EMF of the source - EMF of the battery) / Current
Given:
EMF of the source (E_s) = 30 volts
EMF of the battery (E_b) = 6.3 volts
Current (I) = 20 amperes
Calculating the resistance needed:
Resistance (R) = (E_s - E_b) / I
= (30 - 6.3) / 20
= 23.7 / 20
= 1.185 ohms
Therefore, the resistance needed is approximately 1.185 ohms.
b. To calculate the cost of electrical energy used, we need to find the total energy consumed and then calculate the cost based on the given price per kilowatt-hour.
First, we need to find the total energy consumed. The formula is:
Energy Consumed (E) = Voltage * Current * Time
Given:
Voltage (V) = 30 volts
Current (I) = 20 amperes
Time (t) = 120 amperes-hours
Converting time to hours:
120 amperes-hours / 20 amperes = 6 hours
Calculating the energy consumed:
E = V * I * t
= 30 * 20 * 6
= 3600 watt-hours
Converting watt-hours to kilowatt-hours:
3600 watt-hours / 1000 = 3.6 kilowatt-hours
Calculating the cost of electrical energy used:
Cost = Energy Consumed * Cost per Kilowatt-hour
= 3.6 kilowatt-hours * 12.50 Pesos/kilowatt-hour
= 45 Pesos
Therefore, the cost of electrical energy used in charging the battery is 45 Pesos.