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When three resistors connected in a parallel arrangement to a battery, then the
When three resistors connected in a parallel arrangement to a battery, then the
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Solution
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B current will be different through each resistor.
C potential will be same across each resistor.
Components connected in parallel are connected so the same voltage is applied to each component. In parallel circuits, each light has its own circuit, so all but one light could be burned out, and the last one will still function.
Figure 1 shows a combination of resistors in which three resistors are connected together between points X and Y. Here, the resistors are said to be connected in parallel.
Experiment to show that the same potential difference (voltage) exists across three resistors connected in a parallel arrangement to a battery:
Objects Required:
Make a parallel combination, XY, of three resistors having resistances R1, R2, and R3, respectively. Connect it with a battery, a plug key and an ammeter, as shown in Figure 1. Also connect a voltmeter in parallel with the combination of resistors.
Experiment:
Plug the key and note the ammeter reading.Let the current be I. Also take the voltmeter reading. It gives the potential difference V, across the combination. The potential difference across each resistor is also V. This can be checked by connecting the voltmeter across each individual resistor.
Now, take out the plug from the key. Remove the ammeter and voltmeter from the circuit. Insert the ammeter in series with the resistor R1, as shown in Figure 2. Note the ammeter reading, I1.
Similarly, measure the currents through R2 and R3. Let these be I2 and I3, respectively.
Observation:
It is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination.
I = I1 +I2 + I3 (1) Let Rp be the equivalent resistance of the parallel combination of resistors. By applying Ohms law to the parallel combination of resistors, we have
I = V/Rp (2) On applying Ohms law to each resistor, we have
I1 = V /R1; I2 = V /R2; and I3 = V /R3 (3)From Eqs. (1) to (3), we have
V/Rp = V/R1 + V/R2 + V/R3
Or
1/Rp = 1/R1 + 1/R2 + 1/R3
Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.
Hence, this proves that the same potential difference (voltage) exists across three resistors connected in a parallel arrangement to a battery.
B current will be different through each resistor.
C potential will be same across each resistor.
Components connected in parallel are connected so the same voltage is applied to each component. In parallel circuits, each light has its own circuit, so all but one light could be burned out, and the last one will still function.
Figure 1 shows a combination of resistors in which three resistors are connected together between points X and Y. Here, the resistors are said to be connected in parallel.
Experiment to show that the same potential difference (voltage) exists across three resistors connected in a parallel arrangement to a battery:
Objects Required:
Make a parallel combination, XY, of three resistors having resistances R1, R2, and R3, respectively. Connect it with a battery, a plug key and an ammeter, as shown in Figure 1. Also connect a voltmeter in parallel with the combination of resistors.
Experiment:
Plug the key and note the ammeter reading.Let the current be I. Also take the voltmeter reading. It gives the potential difference V, across the combination. The potential difference across each resistor is also V. This can be checked by connecting the voltmeter across each individual resistor.
Now, take out the plug from the key. Remove the ammeter and voltmeter from the circuit. Insert the ammeter in series with the resistor R1, as shown in Figure 2. Note the ammeter reading, I1.
Similarly, measure the currents through R2 and R3. Let these be I2 and I3, respectively.
Observation:
It is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination.
I = I1 +I2 + I3 (1) Let Rp be the equivalent resistance of the parallel combination of resistors. By applying Ohms law to the parallel combination of resistors, we have
I = V/Rp (2) On applying Ohms law to each resistor, we have
I1 = V /R1; I2 = V /R2; and I3 = V /R3 (3)From Eqs. (1) to (3), we have
V/Rp = V/R1 + V/R2 + V/R3
Or
1/Rp = 1/R1 + 1/R2 + 1/R3
Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.
Hence, this proves that the same potential difference (voltage) exists across three resistors connected in a parallel arrangement to a battery.
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