Experiment 4. Electric circuit (Wheatstone Bridge)

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Blaze Hamilton
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1 Experiment 4. Electric circuit (Wheatstone Bridge). Purpose Understand the structure and measurement method of Wheatstone Bridge. Measure unknown electric resistances properly. 2. Principle () Theory As shown in Figure (a), Wheatstone bridge is a equipment which measure voltage difference between two point a and b by connecting a galvanometer(g). It has four resistances which are R, R 2, R k and R x. It uses null-comparison method to find equilibrium position by adjusting R, R 2 and Rx which controls current. When we shut down switch button on G, there is no current between a and b. It makes, therefore, equipotential point. It means that V ac =I k R k and V bc =I R is same. These equations are formed I k R k =I R () I x R x =I 2 R 2 (2) All resistances are connected. Since the current which pass through G is 0, () and (2) will be changed by putting I =I 2 and I x =I k, R x /R k =R 2 /R, therefore, R x =R k (R 2 /R ) (3) In Wheatstone bridge, as shown in Fig. (b), R and R2 are composed of uniform resistance wire which has a crosssection (A) and resistivity (ρ). Therefore, resistance wire per unit length is uniform. It satisfies that each resistance R and R 2 are proportional to length. R, which has length I, and R 2, which has length I 2, satisfy following relationship, R =ρi /A, R 2 =ρi 2 /A (4) R2/R=(ρI 2 /A)/(ρI /A)=I 2 /I (5) When (4) is substituted to (3), R x becomes R x =R k (I 2 /I ) (6) Therefore, Rx is well noticed by measuring length I and I 2 with R k value. - -

2 Fig. Wheatstone Bridge - 2 -

Dial mode Wheatstone Bridge The most dial mode Wheatstone bridge has same structure. It s operation will be explained as shown in Fig. 2. The top dial shows the ratio multiply of R 2 /R.

3 Dial mode Wheatstone Bridge The most dial mode Wheatstone bridge has same structure. It s operation will be explained as shown in Fig. 2. The top dial shows the ratio multiply of R 2 /R. R v is composed of 4 dials (x000, x00, x0, x) which are in bottom line with dial number 0 to 9. Resistance R x is connected to a terminal X. Power switch is closed by putting BA button with adjusting ratio multiply dial and R v. While it is connecting by putting GA switch button, we should watch the needle on screen. Fig 2. Dial mode Wheatstone Bridge We should find the position of needle which is moving opposition by controlling ratio multiply dial

4 3. Equipment and set up () Wire mode Wheatstone bridge, Dial mode Wheatstone bridge (2) Accurate changeable resistance box (3) High sensitivity galvanometer (4) Power (.5V~3V DC) (5) 3 resistances (with color code) - 4 -

5 4. Experiment & Results Circuit composition () As shown in Fig. (b), wire mode Wheatstone bridge is formed by connecting wire, R k and R x. (2) We should put resistance on R x to measure and changeable resistance box on R k. (3) The ratio R of R 2 is defined as end point (position b) of galvanometer which is determined wire length I and I 2. Resistance Measurement (wire mode Wheatstone bridge, dial mode Wheatstone bridge) We choose resistance one of three color code attached resistances for R x and compare two values; one is measured by bridge method and the other one is color code value. (4) Record average resistance value R n and tolerance on Table by checking color code on R x. (5) Connect this resistance on R x circuit position. (6) Adjust changeable resistance box in order to have same values R k and R n. (7) Confirm the circuit before turn on power for safety. (8) Turn on power switch and adjust input voltage to ~2V. (9) Find the position which indicates zero current flowing by moving end point of galvanometer. (0) Put K2 to be on for removing protection mode of galvanometer and move position b by adjusting precisely which indicates no zero current flowing. () After find position b, record wire length I and I 2 on Table. (2) Repeat (9), (0) and () measurement with changing R k value to be R n s /2 and 2 times. (3) Calculate R x value and confirm tolerance with average value R n. (4) Repeat all experiments with different two resistances and measure resistances. Measure resistance by using dial mode Wheatstone bridge

6 Resistance A Resistance B Resistance C General Physics ExperimentⅡ, Department of Physics, Sogang University 5. DATA SHEET ) Wire mode Wheatstone bridge Exp. R k R n (%) Wire location(cm) I I 2 I 2 /I R x (R n -R x ) /2 2 /2 2 /2 2 resistance = R n X % () - 6 -

7 Resistance A Resistance B Resistance C General Physics ExperimentⅡ, Department of Physics, Sogang University 2) Dial mode Wheatstone bridge Exp. R 2 /R R n (%) R k R x (R n -R x ) resistance = R n X % () 6. Question ) Is the measured resistance in tolerance range? What if, why does it happen? 2) How can we increase accuracy of resistance measurement putting I 2 /I ratio? - 7 -

SOURCES OF EMF AND KIRCHHOFF S LAWS

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