Advertisements
Advertisements
प्रश्न
Explain the equivalent resistance of a parallel resistor network.
Advertisements
उत्तर
Resistors are in parallel when they are connected across the same potential difference as shown in the following figure.
Three resistors in parallel
In this case, the total current I that leaves the battery in split into three separate paths. Let I1, I2 and I3 be the current through the resistors R1, R2 and R3 respectively. Due to the conservation of charge, total current in the circuit I is equal to sum of the currents through each of the three resistors.
I = I1 + I2 + I3 ……. (1)
Since the voltage across each resistor is the same, applying Ohm’s law to each resistor, we have
`"I"_1 = "V"/"R"_1, "I"_2 = "V"/"R"_2, "I"_1 = "V"/"R"_3`
Substituting these values in equation (1), we get
I = `"V"/"R"_1 + "V"/"R"_2 + "V"/"R"_3`
= V`[1/"R"_1 + 1/"R"_2 + 1/"R"_3]`
I = `"V"/"R"_"p"`
`1/"R"_"p" = 1/"R"_1 + 1/"R"_2 + 1/"R"_3`
Here RP is the equivalent resistance of the parallel combination of the resistors. Thus, when a number of resistors are connected in parallel, the sum of the reciprocal of the values of resistance of the individual resistor is equal to the reciprocal of the effective resistance of the combination as shown in the following figure.
Equivalent resistance (RP) has the same current
APPEARS IN
संबंधित प्रश्न
Write the SI unit of resistivity
The unit of electrical resistance is:
(a) ampere
(b) volt
(c) coulomb
(d) ohm
How much energy is consumed when a current of 5 amperes flows through the filament (or element) of a heater having resistance of 100 ohms for two hours? Express it in joules.
In an experiment of verification of Ohm’s law following observations are obtained.
|
Potential difference V (in volt) |
0.5 | 1.0 | 1.5 | 2.0 | 2.5 |
| current I (in ampere) | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
Draw a V-I graph and use this graph to find:
- the potential difference V when the current I is 0.5 A,
- the current I when the potential difference V is 0.75 V,
- the resistance in a circuit.
A wire of resistance 9 ohm having length 30 cm is tripled on itself. What is its new resistance?
Calculate the effective resistance across AB?
Fig. represents the circuit used for the verification of ohm's law. Label the different parts from A and F. State the function of each.
- Name and state the law which relates the potential difference and current in a conductor.
- What is the necessary condition for a conductor to obey the law named above in part (a) ?
Draw a neat diagram for the verification of Ohm’s law by voltmeter-ammeter method. By another diagram show the relation between p.d. and current.
Obtain the macroscopic form of Ohm’s law from its microscopic form and discuss its limitation.
