Advertisements
Advertisements
प्रश्न
Obtain the balancing condition for the Wheatstone bridge arrangements as shown in Figure 4 below:
Advertisements
उत्तर
Let `I_3` and `I_4` be the currents in resistors Q and S respectively . Let `I_g` be the current through galvanometer. For balanced condition,
`I_g = 0`
Applying junction law at ‘b’ we get
`I_1 = I_3 + I_g`
`because I_g = 0 , I_1 = I_3` ....(i)
Applying junction law at ‘d’, we get
`I_2 + I_g = I_4`
`because I_g = 0 , I_2 = I_4` ....(ii)
Applying loop law in the loop abda, we get
`-I_1·P - I_g·Q + -I_2·R = 0`
⇒ `-I_1P + I_2R = 0` (`because I_g = 0`)
⇒ `I_1P = I_2R`
⇒ `P/R = I_2/I_1` ....(iii)
Applying loop law in the loop bcdb, we get
`-I_3·Q + I_4·S + I_g·6 = 0`
⇒ `-I_3·Q + I_4·S + 0 = 0 (because I_g =0)`
⇒ `-I_3Q = I_4S`
⇒ `Q/S = I_4/I_3`
⇒ `Q/S = I_2/I_1` ...(iv) [using eq.(i) and (ii)]
From eq. (iii) and (iv), `P/ R = Q/s`
⇒ `P/Q = R/S`
This is the balanced condition.
APPEARS IN
संबंधित प्रश्न
With the help of a labelled diagram, show that the balancing condition of a Wheatstone bridge is
`R_1/R_2 = R_3/R_4` where the terms have their usual meaning.
Explain with a neat circuit diagram. How you will determine the unknown resistances using a meter bridge.
In a metre bridge, the gaps are closed by two resistances P and Q and the balance point is obtained at 40 cm. When Q is shunted by a resistance of 10 Ω, the balance point shifts to 50 cm. The values of P and Q are ______
In a metre bridge experiment. the ratio of the left-gap resistance to right gap resistance is 2: 3. The balance point from the left is ______.
A resistance of 5 `Omega` is connected in the left gap of a metre bridge and 15 `Omega` in the other gap. The position of the balancing point is ____________.
The potential difference between the points A and B in the electric circuit shown is ______.
In the meter bridge experiment, the null point is obtained at a distance of ℓ from the left end. The resistance in the left and right gaps are halved and then interchanged. The new position of the null point is at ______
When an unknown resistance 'X' is connected in the left gap of a meter bridge and a known resistance 'R' in the right gap, a null point is obtained at 40 cm from the left end. If a 2 Ω resistance is connected in series with 'X' the null point shifts towards the right by 10 cm, with some resistance in the right gap. The value of 'X' must be ______
Find the radius of the wire of length 25m needed to prepare a coil of resistance 25Ω. (Resistivity of material of wire is 3.142 x 10-7Ωm)
