Question

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

If I₁/I₀=4/5, find I₂/I₀.

Express the ratio I₂/I₀ numerically.

I₂/I₀ =

Answer 1

If I1 / I0 = 4/5, find I2 / I0.
Express the ratio I2 / I0 numerically.

Since I1 / I0 = 4/5, we can say that I1 = 4 and I0 = 5. We also know that V = IR and I = V/R. Say that Ru = 1. That means that I0 = 5 = V / 1, so V = 5. So for I1:

V = IR

The resistors are in series, so:

5 = 4 * (Ru + Rr)
5 = 4 * (1 + Rr)
Rr = 0.25

We can apply this to I2 (again, the resistors are in series, so we add them):

V = I2 * R
V = I2 * (Rr + Rr + Ru)
5 = I2 (1.5)
I2 = 3.333

So I2 / I0 = 3.333 / 5 = 0.667