A 10 ohm, 20 ohm lamp and 12v battery are connected in a parallel. A current of 1.8 A passes through the battery and a current of 1.2 A passes through the motor.
1) Determine the current through the lamp.
2) Calculate the potential difference across the motor.
3) is this the total resistance of the circuit is greater or smaller than 10 ohms.
R1 = 10 Ohms.
R2 = 20 Ohms.
I1 = 1.2A.
1. I1 + I2 = 1.8A.
1.2 + I2 = 1.8, I2 = 0.6A.
2. V = I1*R1 = 1.2 * 10 = 12 Volts.
3. Rt = R1*R2/(R1+R2) = 10*20/(10+20) = 6.67 Ohms.
To determine the current through the lamp, we first need to calculate the total resistance of the circuit.
1) Calculate the total resistance in the circuit:
Since the lamp and motor are connected in parallel, we can use the formula for calculating the total resistance in a parallel circuit:
1/total resistance = 1/20 + 1/12
To simplify the equation, we can find the least common multiple (LCM) of 20 and 12, which is 60.
1/total resistance = 3/60 + 5/60
1/total resistance = 8/60
To find the total resistance, take the reciprocal of both sides:
total resistance = 60/8
total resistance = 7.5 ohms
2) Calculate the current through the lamp:
Using Ohm's Law (V = I × R), we can calculate the current passing through the lamp:
I (current) = V (potential difference) / R (resistance)
I (lamp) = 12 V / 10 Ω
I (lamp) = 1.2 A
The current passing through the lamp is 1.2 A.
3) Determine if the total resistance of the circuit is greater or smaller than 10 ohms:
We have already calculated the total resistance of the circuit as 7.5 ohms. Therefore, the total resistance is smaller than 10 ohms.
To solve this question, we can use Ohm's Law and the principles of parallel circuits.
1) To determine the current through the lamp, we need to find the total current passing through the parallel circuit. In a parallel circuit, the total current is the sum of the individual branch currents. Therefore, we can add up the currents passing through the battery and the motor:
Total current = current through battery + current through motor
Total current = 1.8 A + 1.2 A
Total current = 3 A
Now that we have the total current, we can find the current passing through the lamp. Since the parallel circuit splits the current, the current passing through each branch is the same. Therefore, the current passing through the lamp is also 3 A.
2) To calculate the potential difference (voltage) across the motor, we can use Ohm's Law. Ohm's Law states that the voltage across a component is equal to the product of its resistance and the current passing through it. In this case, the resistance of the motor is given as 20 ohms, and the current passing through it is 1.2 A:
Potential difference across motor = Resistance of motor × Current through motor
Potential difference across motor = 20 ohms × 1.2 A
Potential difference across motor = 24 volts
Therefore, the potential difference across the motor is 24 volts.
3) To determine if the total resistance of the circuit is greater or smaller than 10 ohms, we need to calculate the equivalent resistance of the circuit. In a parallel circuit, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. In this case, we have two resistors in parallel: a 10 ohm and a 20 ohm resistor.
1/Total resistance = 1/10 ohms + 1/20 ohms
1/Total resistance = 2/20 + 1/20
1/Total resistance = 3/20
Total resistance = 20/3 ohms
The total resistance of the circuit is approximately 6.67 ohms, which is smaller than 10 ohms.