Question

The terminals of a battery are connected across two resistors in series. The resistances of the resistors are not the same. Which of the following statements are correct? Choose all that are correct. (a) The resistor with the smaller resistance carries more current than the other resistor. (b) The resistor with the larger resistance carries less current than the other resistor. (c) The current in each resistor is the same. (d) The potential difference across each resistor is the same. (e) The potential difference is greatest across the resistor closest to the positive termina

Answer 1

Answer:

(c) The current in each resistor is the same.

Explanation:

When two resistors are connected in series, we have the following:

- The resistors are connected such that the current passing through the two resistors is the same

- The voltage of the battery is equal to the sum of the voltage drops across each resistor

- the equivalent resistance of the circuit is equal to the sum of the individual resistances:

R = R1 + R2

So, let's analyze each statement:

(a) The resistor with the smaller resistance carries more current than the other resistor. --> FALSE. The current through the two resistors is the same.

(b) The resistor with the larger resistance carries less current than the other resistor. --> FALSE. The current through the two resistors is the same.

(c) The current in each resistor is the same. --> TRUE.

(d) The potential difference across each resistor is the same. --> FALSE: the potential difference across each resistor is given by

V=RI

where I (the current) is the same for both resistors, while R (the resistance) is not, so V is also different for the two resistors.

(e) The potential difference is greatest across the resistor closest to the positive terminal --> FALSE. According to

V=RI

the potential difference depends only on the value of the resistance, so it doesn't matter which resistor is connected to the positive terminal.