Equivalent Resistance (10th-Physics-Lesson-16. 4) Part 3

Physics 3 minutes read
  1. The equivalent resistance  of a series combination is that resistance which when substituted in place of the combination, the same current woud flow through the circuit. Fig. 16. 10 shows the equivalent resistance Re. Note that the battery is sending the same current, which it was sending when the combination was connected in the circuit.

By ohm’s law.

eqivalent_resistance

current-woud-flow-through-the-circuit

Fig. 16. 10

Thus the equivalent resistance of a series combination is equal to the sum of the individual resistances of the combination.

If resistances , resistances_connected are connected in series then their equivalent resistance Re can be determined by the following equation.

following_equation

Example 16.4: in a series circuit, if the value of resistors value_of_resistorsrespectively and the voltage of battery is 10V, then find the following quantities.

  1. Equivalent resistance of the series combination.
  2. The current flowing through each of the resistance.
  3. Potential difference across each of the resistance

Solution:

series_combination

  1. If a battery of10V is connected across the equivalent resistance, the current passing through it is given by

connected across

According to definition of equivalent resistance same current would pass through each resistance of the series combination.

accoridng to definition

Do you know?

electronic-circuits

Resistances of different values are important component of electronic circuits.

  1. Parallel combination of resistances

In this combination, resistances are connected in such a way that one end of all the resistors is connected to one point, say ‘A’ and all the other ends to another point ‘B’ as shown in Gig. 16.11 (a). In the circuit thus formed, several paths are available for the flow of current. The total current of the circuit is divided in these paths. The parallel combination has the following characteristic features:

Parallel-combination-of-resistances

Fig. 16.11 (a)

  1. In this combination, the potential drop across all the resistances is the same. In fig. 16. 11(a), the potential drop across each of the resistance will be V.
  2. The sum of the current flowing through the various resistances of this combination is equal to the total current of the circuit. In fig. 16. 11(a)

potential_drop_across

  1. The equivalent resistance Re of the parallel combination is that resistance which when substituted in place of the parallel combination does not alter the total current of the circuit (fig. 16. 11-b).

by_ohm's_law

total-current-of-the-circuit

Fig. 16. 11 (b)

If resistancesconnected in parallel  Are connected in parallel, then their equivalent resistance can be determined by the following equation:

derermined _equation

Example 16.5: if in the circuit shown in fig. 16. 11(a) circuit_shown then find the following quantities:

  1. Equivalent resistance of the circuit.
  2. Current flowing through each of the resistance.
  3. The total current of the circuit.

Solution:

If Re is the equivalent resistance of the parallel combination, then

parallel combination

Note that the value of the equivalent resistance of the parallel combination is smaller than the lowest value of the resistance used in this combination.

  1. As the resistances are connected in parallel, so the potential difference across each of the resistance would be equal to the potential V = 6V of the battery.

current_passing_through

As the sum of the current passing through the resistances of parallel combination is equal to the total current I of the circuit. Therefore

circuit