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Battery, Ammeter, and Resistors

An ammeter is connected in series to a battery of voltage Vb and a resistor of unknown resistance Ru (Figure 1) . The ammeter reads a current I0. Next, a resistor of unknown resistance Rr is connected in series to the ammeter, and the ammeter's reading drops to I1. Finally, a second resistor, also of resistance Rr, is connected in series as well. Now the ammeter reads I2.

Part A

If I1/I0=4/5, find I2/I0.

Express the ratio I2/I0 numerically.

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Battery, Ammeter, and Resistors

An ammeter is connected in series to a battery of voltage Vb and a resistor of unknown resistance Ru (Figure 1) . The ammeter reads a current I0. Next, a resistor of unknown resistance Rr is connected in series to the ammeter, and the ammeter's reading drops to I1. Finally, a second resistor, also of resistance Rr, is connected in series as well. Now the ammeter reads I2.

Part A

If I1/I0=4/5, find I2/I0.

Express the ratio I2/I0 numerically.

Hints

Explanation / Answer

Part A )

using figure 1

the current is Io = Vb / Ru

and

I1 = Vb / Ru + Rr

sameway is

I2 = Vb / Ru + 2 Rr

given is

I1 / Io = 4/5

then

( Vb / Ru + Rr ) / ( Vb / Ru ) = 4/5

Ru = 4 Rr

I2 / Io = ( Vb / Ru + 2 Rr ) / ( Vb / Ru )

I2 / Io = 2/3

I2 / Io = 0.667

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