# A 5.0 Ω resistor is hooked up in series with a 10.0 Ω resistor followed by a 20.0 Ω resistor. The circuit is powered by a 9.0 V battery. A) Calculate the voltage drop across each resistor in the...

A 5.0 Ω resistor is hooked up in series with a 10.0 Ω resistor followed by a 20.0 Ω resistor. The circuit is powered by a 9.0 V battery.

A) Calculate the voltage drop across each resistor in the circuit.

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### 1 Answer

When the three resistors are connected in series, the equivalent resistance of the circuit is

``

So the equivalent resistance of the given circuit is ``

Then the current in the circuit, and through each of the resistors, is determined by

`` , where U is the voltage supplied by the battery.

(When the resistors are in series, the current through each resistor is the same.)

`i=(9V)/(35Omega) = 9/35 A`

The voltage drop across each resistor is the current through the resistor times resistance:

`U_1 = iR_1 =(9/35)*5=9/7 V`

`U_2=iR_2 = (9/35)*10=18/7 V`

`U_3=iR_3 = (9/35)*20=36/7 V`

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