Advertisements
Advertisements
Question
Obtain the balancing condition for the Wheatstone bridge arrangements as shown in Figure 4 below:
Advertisements
Solution
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
RELATED QUESTIONS
What should be the value of R in the figure for which the current in it is zero?
With resistances P and Q placed in the left and right gaps of a metre bridge, the balance point divides the wire in the ratio of 1/3. When P and Q are increased by 40 n each. the balance point divides the wire in the ratio of 3/5. The values of P and Q will be respectively, ______
In a metre bridge experiment, the null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y?
In the network shown cell E has internal resistance r and the galvanometer shows zero deflection. If the cell is replaced by a new cell of emf 2E and internal resistance 3r keeping everything else identical, then ______.
ln, a Wheatstone network, P = Q = R = 8 `Omega` and S is 10 `Omega`. The required resistance to be connected to S so that network is balanced is ______.
The resistances in left and right gap of a meter-bridge are 3 `Omega` and 5 `Omega` respectively. When the resistance in the left gap is increased by 10%, the balance point shifts nearly by ______.
In a Wheatstone's bridge, the resistance in the three arms are P, Q, R, and its fourth arm has a parallel combination of two resistances S1 and S2, The balancing condition of the bridge is ______
Draw a neat labelled diagram to determine unknown resistance using a meter bridge.
Draw a neat labelled diagram of Kelvin's meter bridge circuit for the measurement of galvanometer resistance.
In a Wheatstone’s bridge, three resistances P, Q and R connected in the three arms and the fourth arm is formed by two resistances S1 and S2 connected in parallel. The condition for the bridge to be balanced will be ______.
