Distribution of Current in Two Resistors in Parallel
Distribution of Current in Two Resistors in Parallel
In the case of a parallel combination of resistance the current is divided into different paths and the sum of current passing through each resistance is equal to the total current through the circuit. Now let us derive a relation between current and resistance to calculate the amount of current passing through each resistance. In the circuit below we have two resistance R1 and R2 connected in parallel.
The resistors R1 and R2 are connected in parallel. The current I gets distributed in the two resistors. Let I1 and I2 be the current flowing through the resistors R1 and R2 respectively. As the resistance are connected in parallel so the sum of the current flowing through two resistance is equal to the total current flowing in the circuit. So we have
. (i)
Applying Ohm s law to the resistor ,
(ii)
And applying Ohm s law to the resistor ,
. (iii)
From (ii) and (iii) we get
.
Substituting for I2 in (i), we have
or
Similarly,
Thus,
The current through each branch in a parallel combination of resistors is inversely proportional to its resistance.
Illustration: Two resistors of resistances R1 and R2 having resistance 10 ohms and 20 ohms respectively are connected in parallel. A battery supplies 6 A of current to the combination, as shown in fig. Calculate the current in each resistor.
Solution: As the two resistance are connected in parallel the current in the resistance can be calculated as follows
The current in the resistor is
The current in the resistor is
The potential difference between the terminals of an electric heater is 50 V when it draws a current of 6 A from the source.What current will the heater draw if the potential difference is increased to 110 V ? | |||
| Right Option : C | |||
| View Explanation | |||
In parallel combination of resistance the total current flowing through the circuit is equal to _____________________________.
| |||
| Right Option : B | |||
| View Explanation | |||
Two resistors are connected in series to 25 volt battery, and an ammeter in the circuit reads 0.50 A. The first resistor is rated at 22 ohms. Find :- (a) the total resistance (b) the resistance of the second resistor (c) the potential difference across the second resistor. | |||
| Right Option : C | |||
| View Explanation | |||
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