Advertisements
Advertisements
प्रश्न
Suppose there are three resistors A, B, and C having resistances r1, r2, and r3 respectively. If R represents their equivalent resistance, establish the following relation `1/"R" = 1/"r"_1 + 1/"r"_2 + 1/"r"_3`, when joined in parallel.
Advertisements
उत्तर
When joined in parallel, let the main current be i which sub-divides at P into i1 in r1, i2 in r2 and i3 in r3 respectively in given figure.
If potential difference across PQ be V then,
According to Ohm's law:
i1 = Vr1 ...(i)
i2 = Vr2 ....(ii)
and i3 = Vr3 ...(iii)
If R'' be the equivalent resistance of this combination, then
i = `"V"/"R''"` ....(A)
From (i), (ii) and (iii) on adding, we get ....(B)
i = i1 + i2 + i3
`= "V"/"r"_1 + "V"/"r"_2 + "V"/"r"_3`
`= "V"(1/"r"_1 + 1/"r"_2 + 1/"r"_3)`
Comparing (A) and (B)
`"V"/"R''" = "V"(1/"r"_1 + 1/"r"_2 + 1/"r"_3)`
or `1/"R''" = 1/"r"_1 + 1/"r"_2 + 1/"r"_3`
संबंधित प्रश्न
State two causes of energy loss in a transformer.
You have three resistors of values 2Ω, 3Ω and 5Ω. How will you join them so that the total resistance is more than 7Ω?
1) Draw a diagram for the arrangement
2) Calculate the equivalent resistance.
A potential difference of 20 volts is applied across the ends of a resistance of 5 ohms. What current will flow in the resistance?
Keeping the potential difference constant, the resistance of a circuit is doubled. By how much does the current change?
What p.d. is needed to send a current of 6 A through an electrical appliance having a resistance of 40 Ω?
The potential difference between the terminals of an electric iron is 240 V and the current is 5.0 A. What is the resistance of the electric iron?
In the circuit shown below:
The potential difference across the 3 Ω resistor is:
Which of the following represents voltage?
A current of 1 ampere flows in a series circuit containing an electric lamp and a conductor of 5 Ω when connected to a 10 V battery. Calculate the resistance of the electric lamp.
Now if a resistance of 10 Ω is connected in parallel with this series combination, what change (if any) in current flowing through 5 Ω conductor and potential difference across the lamp will take place? Give reason.
Two charged spherical conductors of radius R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres (σ1/σ2 ) is ______
