Four 20 ohm resistors are connected in series and the combination is connected to a 20V emf device. The potential difference across any one of the resistors is:

Question

Four 20 ohm resistors are connected in series and the combination is connected to a 20V emf device. The potential difference across any one of the resistors is:

A) 1 V
B) 4 V
C) 5 V
D) 20V
E) 80 V

So there are four resistors that are 20 ohms. Their connected to a 20 V device. The question wants to known volts. Its says for a parallel circuit. I just divided 20V/4 and got 5V.Is that ok to think of it that way?

correct on the first. However, if the second circuit is parallel, each resistor has 20V across it.

The second circuit is in series.

Thank you

correct.

Answer 1

To find the potential difference across each resistor, we can use the concept of series circuits. In a series circuit, the total potential difference (V_total) is equal to the sum of the potential differences across each individual component.

In this case, we have four resistors connected in series with a 20V emf device. Since the resistors are in series, the potential difference across each resistor will be the same. Let's call it V_resistor.

Now, we can use Ohm's Law to find the value of V_resistor. Ohm's Law states that the potential difference across a resistor (V_resistor) is equal to the current flowing through the resistor (I_resistor) multiplied by the resistance of the resistor (R_resistor).

In this question, the current flowing through each resistor is the same, as it is a series circuit. So, we can write V_resistor = I_resistor * R_resistor.

Since the question doesn't provide the current value, we can use the fact that the total potential difference across the series circuit (V_total) is 20V and the total resistance (R_total) is the sum of the resistances of the individual resistors, which is 4 * 20 ohms = 80 ohms.

Using Ohm's Law again, we can write V_total = I_total * R_total. Rearranging the equation, we get I_total = V_total / R_total.

Substituting the given values, we have I_total = 20V / 80 ohms = 0.25 A (amperes).

Since the current is the same in a series circuit, the current flowing through each resistor is 0.25 A.

Now, we can calculate the potential difference across each resistor (V_resistor) using Ohm's Law: V_resistor = I_resistor * R_resistor.

Substituting the known values, we have V_resistor = 0.25 A * 20 ohms = 5 V.

Therefore, the potential difference across each resistor is 5 V.

Hence, the correct answer is C) 5 V.