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
A low voltage supply from which one needs high currents must have very low internal resistance. Why?
The relationship between the potential difference and the current in a conductor is stated in the form of a law.
- Name the law.
- What does the slope of V-I graph for a conductor represent?
- Name the material used for making the connecting wire.
What is an ohmic resistor? Give one example of an ohmic resistor. Draw a graph to show its current voltage relationship. How is the resistance of the resistor determined from this graph?
Define ampere and volt with respect to Ohm’s law.
Ohm’s law states the relationship between power and voltage.
State macroscopic form of Ohm’s law.
How is electric current related to the potential difference across the terminals of a conductor?
Draw a labelled circuit diagram to verify this relationship.
Ohm's Law states that for a metallic conductor, the current flowing through it is directly proportional to the potential difference across its ends, provided that:
From Ohm's Law, since \[I \propto V\], the constant ratio \[\frac{V}{I}\] is defined as:
