A circuite has the resistors (R_1, R_2, and R_3) in parallel. This group is in s

Question

A circuite has the resistors (R_1, R_2, and R_3) in parallel. This group is in series with R_4. The equivalent resistance is: a. R_4 + 1 (1/R_1 + 1/R_2 + 1/R__3_b) (1/R_1 + 1/R_2 + 1/R_3) + R_4 c. (R_1 + R_2 + R_3) + 1/R_4 d. R_1 + R_2 + R_3 + R_4 e. 1/(R_1 + R_2 + R_3 + R_4) In a circuit powered by a battery, several resistors are connected mparalW. a) The voltage drop across each of these resistors is the same. b) The current in each of these resistors is the same. C) The power dissipated in each of these resistors is the same, d) The voltage drops across these resistors sums to zero. c) The sum of the currents in these resistors is zero.

Explanation / Answer

Hi,

First question

We know that the equivalent resistance can be calculated as follows:

Req = R1 + R2 + ........ (in series)

1/Req = 1/R1 + 1/R2 + ......... (in parallel)

Therefore, if the resistance 1, 2 and 3 are in parallel, the equivalent resistance of them is:

1/R = 1/R1 + 1/R2 + 1/R3 :::::::::: R = 1/( 1/R1 + 1/R2 + 1/R3 )

Finally, if the resistance R is in series with R4, then the total equivalent resistance of the group is:

Req = R4 + R ::::::::: Req = R4 + 1/( 1/R1 + 1/R2 + 1/R3 )

So the answer is letter a.

Second question

In this case the answer is letter a. The reason is because the principal feature of a circuit in parallel is that the potential difference is equal through all the elements. The previous statement can be rewritten as it appears in the problem (the voltage drop across each resistor is the same).

For the other options:

Letter b. The current is the same through all the elements if the circuit is in series.

Letter c. The power dissipated by a resistor depends on the current and the voltage.

Letter d. The voltage decreases across a resistor, so the sum of those changes cannot be zero.

Letter e. The current is always positive by convention, so it cannot be zero.

I hope it helps.

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