Name: Resistivity and Its Temperature Dependence
Uploaded: 2019-07-19
Duration: 5 min 51 s
Description: In this video, we will discuss the resistivity of different materials and the variation of resistivity with temperature. Let us watch this video and learn.

Question

Derive the expression to find the unknown resistance in the balance condition of wheatstone bridge

Accepted Answer

In wheatstone $'$ s bridge, four resistances are joined to form a parallelogram. In one diagonal of this parallelogram a galvanometer is attached, and in other diagonal, a cell. The values of resistances are so adjusted that no current flows through the galvanometer. This condition of bridge is called balanced wheatstone $'$ s bridge condition. Let $P, Q, R and S$ resistances forms a bridge. Let a current, $I$ flows through the circuit.

Applying Kirchhoff $'$ s second law to closed loop $ABDA$ ,

$I_{1} P - I_{2} R = 0 or I_{1} P = I_{2} R$ $‐ equation (1)$

Applying Kirchhoff $'$ s second law to closed loop $BCDB$

$I_{1} Q - I_{2} S = 0 or I_{1} Q = I_{2} S ‐ equation (2)$

Dividing equation $(1)$ by equation $(2)$ , we get

$\frac{I_{1} P}{I_{1} Q} = \frac{I_{2} R}{I_{2} S}$

$\Rightarrow \frac{P}{Q} = \frac{R}{S}$

This is the balanced wheatstone bridge condition.

If $R$ is the unknown resistance, $P$ and $Q$ are the ratio arm of the bridge and $S$ is the standard arm, then $R = \frac{P}{Q} \times S$ .

Derive the expression to find the unknown resistance in the balance condition of wheatstone bridge

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