## Wheatstone bridge – wikipedia electricity quiz ks2

In the figure, R x {\displaystyle \scriptstyle R_{x}} is the unknown resistance to be measured; R 1 , {\displaystyle \scriptstyle R_{1},} R 2 , {\displaystyle \scriptstyle R_{2},} and R 3 {\displaystyle \scriptstyle R_{3}} are resistors of known resistance and the resistance of R 2 {\displaystyle \scriptstyle R_{2}} is adjustable. The resistance R 2 {\displaystyle \scriptstyle R_{2}} is adjusted until the bridge is "balanced" and no current flows through the galvanometer V g {\displaystyle \scriptstyle V_{g}} . At this point, the voltage between the two midpoints ( B and D) will be zero. Therefore the ratio of the two resistances in the known leg ( R 2 / R 1 ) {\displaystyle \scriptstyle (R_{2}/R_{1})} is equal to the ratio of the two in the unknown leg ( R x / R 3 ) {\displaystyle \scriptstyle (R_{x}/R_{3})} . If the bridge is unbalanced, the direction of the current indicates whether R 2 {\displaystyle \scriptstyle R_{2}} is too high or too low.

Detecting zero current with a galvanometer can be done to extremely high precision. Therefore, if R 1 , {\displaystyle \scriptstyle R_{1},} R 2 , {\displaystyle \scriptstyle R_{2},} and R 3 {\displaystyle \scriptstyle R_{3}} are known to high precision, then R x {\displaystyle \scriptstyle R_{x}} can be measured to high precision. Very small changes in R x {\displaystyle \scriptstyle R_{x}} disrupt the balance and are readily detected.

Alternatively, if R 1 , {\displaystyle \scriptstyle R_{1},} R 2 , {\displaystyle \scriptstyle R_{2},} and R 3 {\displaystyle \scriptstyle R_{3}} are known, but R 2 {\displaystyle \scriptstyle R_{2}} is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of R x , {\displaystyle \scriptstyle R_{x},} using Kirchhoff’s circuit laws. This setup is frequently used in strain gauge and resistance thermometer measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage. Derivation [ edit ]

Then, Kirchhoff’s second law is used for finding the voltage in the loops ABD and BCD: ( I 3 ⋅ R 3 ) − ( I G ⋅ R G ) − ( I 1 ⋅ R 1 ) = 0 ( I x ⋅ R x ) − ( I 2 ⋅ R 2 ) + ( I G ⋅ R G ) = 0 {\displaystyle {\begin{aligned}(I_{3}\cdot R_{3})-(I_{G}\cdot R_{G})-(I_{1}\cdot R_{1})&=0\\(I_{x}\cdot R_{x})-(I_{2}\cdot R_{2})+(I_{G}\cdot R_{G})&=0\end{aligned}}}

When the bridge is balanced, then I G = 0, so the second set of equations can be rewritten as: I 3 ⋅ R 3 = I 1 ⋅ R 1 I x ⋅ R x = I 2 ⋅ R 2 {\displaystyle {\begin{aligned}I_{3}\cdot R_{3}&=I_{1}\cdot R_{1}\\I_{x}\cdot R_{x}&=I_{2}\cdot R_{2}\end{aligned}}}

If all four resistor values and the supply voltage ( V S) are known, and the resistance of the galvanometer is high enough that I G is negligible, the voltage across the bridge ( V G) can be found by working out the voltage from each potential divider and subtracting one from the other. The equation for this is: V G = ( R 2 R 1 + R 2 − R x R x + R 3 ) V s {\displaystyle V_{G}=\left({R_{2} \over {R_{1}+R_{2}}}-{R_{x} \over {R_{x}+R_{3}}}\right)V_{s}}

The Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure capacitance, inductance, impedance and other quantities, such as the amount of combustible gases in a sample, with an explosimeter. The Kelvin bridge was specially adapted from the Wheatstone bridge for measuring very low resistances. In many cases, the significance of measuring the unknown resistance is related to measuring the impact of some physical phenomenon (such as force, temperature, pressure, etc.) which thereby allows the use of Wheatstone bridge in measuring those elements indirectly.