In the figure below, a voltmeter of resistance RV-300 , and an ammeter of resist

Question

In the figure below, a voltmeter of resistance RV-300 , and an ammeter of resistance RA 3.00 are being used to measure a resistance R in a circuit, that also contains a resistance R0 = 100 and an ideal battery of emf -18.0 v. Resistance R is given by R v , where v s the voltmeter readin and Sthe current in resistance R However, the ammeter reading is not i, but rather , which is , plus the current through the voltmeter. Thus, the ratio of the two meter readings is not R, but only an apparent resistance R' = Vr If R 75.0 : (a) What is the ammeter reading? (b) What is the voltmeter reading? (c) What is R? a) Ir Av is increased, does the aiference between R and R decrease tay the same

Explanation / Answer

given, voltmeter resistance Rv = 300 ohms

ammeter resistance Ra = 3 ohm

Ro = 100 ohm

R = ?

ideal battery E = 18 V

R = V/i

ammeter reading = i'

R' = V/i'

a. if R = 75 ohm

a. Reff = Ro + Ra + R*Rv/(Ra + Rv)

Reff = 100 + 3 + 75*300/(375) = 163 ohms

hence ammeter reading, i' = E/Reff = 18/163 = 0.1104 A

b. voltmeter reading V = E - i'(Ro + Ra) = 18 - i'(100 + 3)

V = 6.625 V

c. R' = V/i' = (E - i'(Ro + Ra))/i' = E/i' - (Ro + Ra)

R' = E*Reff/E - (Ro + Ra) = R*Rv/(Ra + Rv) = 163 ohms

d. if, Rv is increased, R' - R = R*Rv/(Ra + Rv) - R

R' - R = R[Rv/(Ra + Rv) - 1] = R[Rv - Ra - Rv]/(Ra + Rv) = -R*Ra/(Ra + Rv)

so when Rv increases, R' - R decreases

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---