which a current of 1.70 MA for full-scale defection and has a re of 85.0 10, may

Question

which a current of 1.70 MA for full-scale defection and has a re of 85.0 10, may be used to enable an operator to measure large currents without damage to the galvanometer, a relatively smal shunt resistor is wired in paralel with the gavarometer, Figure 28.27. Most of the current then goes through the shunt resister. Calculate the value of the shunt resistor that al s te gaivan meter to be used to measure .anety 1.00 A at full-scale deflection. (Suggestion: use Kirchhoff s rules.) C) Q-60.0uC 50 40 30 20 10 0 12 3 5 6 uA) 10 (bl 28 Fig

Explanation / Answer

Given

current in the galvanometer is i1 = 1.70 mA

resistance of the galvanometer is R = 85.0 ohm

let shunt resistance is r

the current should be measured by the galvanometer is i2 = 1 A

V = i*R = 1.70*10^-3*85 = 0.1445 V

when the resistance r is connected in parallel to the galvanometer then the the resistance is  

R_eq = R*r/(R+r) = R2

so the current is i1/i2 = R2/R1

R2 = i1*R1 /i2

R*r/(R+r) = R2

(85*r )/(85+r) = (1.70*10^-3*85)/(1) ==> r = 0.14475 ohm

or by shunt resistance formula  

shunt resistance is r = (85*1.7*10^-3)/(1-1.7*10^-3) = 0.14475 ohm

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