Video: Calculating Currents and Voltages in a Series Circuit

The current in the circuit shown is 100 mA. (a) What is the current in the 50 Ω resistor to the nearest milliampere? (b) What is the voltage across the 40 Ω resistor to 2 significant figures? (c) What is the total resistance in this circuit to the nearest ohm?

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Video Transcript

The current in the circuit shown is 100 milliamperes. What is the current in the 50Ω resistor to the nearest milliampere?

We want to know the current in the 50Ω resistor. These resistors are all in series because there’s only one path for the current to take. So before we answer this question, let’s review how voltage and current behave across resistors that are in series. This circuit shows two resistors in series with a voltage 𝑉 and a current 𝐼. Since the same current flows through the entire circuit, the current across both resistors is the same. Since the current across each resistor is the same, according to Ohm’s law which says that the voltage is equal to the current times the resistance, the voltage across each resistor will not be the same. But it will be proportional to the resistance. Though the voltages across each resistor will be different, they will add to the total voltage of the circuit.

Now that we’ve reviewed how current and voltage behave across resistors in series, we know that the current in the 50Ω resistor must be the same as the current in the whole circuit because all of the resistors in this circuit are in series. So the current in the 50Ω resistor to the nearest milliampere is 100 milliamperes.

What is the voltage across the 40Ω resistor to two significant figures?

Now we want the voltage across the 40Ω resistor, which we’ll be able to find using Ohm’s law. As we’ve already established, the current in each resistor in this circuit is the same, 100 milliamperes. And the resistance of the 40Ω resistor is 40Ω. Before we can solve for the voltage, we need to convert the current from milliamperes to amperes. There are 1000 milliamperes in an ampere. So to convert from milliamperes to amperes, we should divide by 1000. Now we can solve for the voltage, which is 4.00 volts, rounding to two significant figures. We’ll find the voltage across the 40Ω resistor is 4.0 volts.

What is the total resistance in this circuit to the nearest ohm?

We can find the total resistance of resistors in series by adding together the resistances of the individual resistors in the circuit. So, we can find the total resistance of this circuit by summing the 30, 40, and 50Ω resistances together. Adding everything together, we’ll find that the total resistance in this circuit is 120Ω.

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