BridgesBridges

Bridge Measurements:

• Bridges are commonly used to measure many quantities (i.e. resistance, inductance, capacitance, …etc).

• The simplest form of a bridge is for the purpose of measuring a resistance which is known as the ((Wheatstone bridge)).

(1)- (1)- Wheatstone bridge:Wheatstone bridge:

Notes:

o The movement here is referred to as a galvanometer.

o The current depends on the voltage difference between nodes c and d. If the voltage difference between c and d is zero then the bridge is said to be balanced. And you may at this point make your measurement.

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Notes:• The Wheatstone bridge is limited to varying from a few ohms (lower limit)

to several mega ohms (upper limit).• In the lower limit, lead and contact resistances are considered.• The upper limit is set by the reduction in sensitivity to unbalance which is

caused by high resistance value, and thus, reducing the current ig .

o Errors in the Wheatstone bridge are in general caused by: (1)- Error in the standard arm ( R3 ) and the ratio arms ( R1 , R2 ).

(2)- Insufficient sensitivity of the null detector (the galvanometer). (3)- Resistance of the leads and contacts.

o It is necessary that the galvanometer has the required sensitivity to detect an unbalance condition. This can be analyzed by investigating the current ig To do this, we use Thevenin’s technique:

• (A)- Thevenin’s equivalent circuit:

• Killing the source ( E ) will yield a short circuit:

• To obtain ( Voc ) :

• And using KVL:

Example: A galvanometer with sensitivity of 10mm/µA . Calculate the

deflection of the galvanometer caused by a 5Ω unbalance in the arm BC.

• Solution:

• (B)-If the battery has no internal resistance:

• While if it does have internal resistance:

• We solve it using transformation.

• Hence,

))22 -( -(kelvin bridgekelvin bridge::• [Effect of the connecting leads].