Question

Which of the following relationships must be true according to the laws of series and parallel connections? (Selectonlyrelationships thatmustbe trueaccording to the laws of series and parallel connections, not those that are true in this problem only because of the particular resistances given.)Check all that apply.

\(I_{1}=I_{3}\)

\(I_{3}=I_{4}\)

\(I_{2}=I_{1}+I_{3}\)

\(I_{1}=I_{3}+I_{2}\)

\(\Delta V_{1}=\Delta V_{2}\)

\(\Delta V_{3}=\Delta V_{4}\)

\(\Delta V_{1}=\Delta V_{3}+\Delta V_{4}\)

\(\Delta V_{2}=\Delta V_{3}+\Delta V_{4}\)

\(\Delta V_{1}=\Delta V_{2}+\Delta V_{3}+\Delta V_{4}\)

Answer 1

Remember:
For series combination
Req = R1 + R2 + R3 + ....
for parallel combination
1/Req = 1/R1 + 1/R2 + 1/R3 + ....
for 2 resistors in parallel it will be
Req = R1*R2/(R1+R2)
Now in given circuit:

Since R3 and R4 are in series, So

R34 = R3 + R4

then R1 and R34 are in parallel, So

R134 = R1*R34/(R1 + R34)

then R2 and R134 are in series, So

Req = R2 + R134 = R2 + (R1*R34/(R1 + R34))

Ieq = V/Req

Also in resistors parallel combination voltage distribution in each part will be the same and in series combination, current distribution in each resistor will be the same.

Resistor R3 and R4 are in series, So Current in both resistors will be equal

I3 = I4

Since R2 and R134 are in series with the battery, So

Ieq = I2 = I134

I134 = I1 + I34

Since R3 and R4 are in series, So I34 = I3 = I4, So

I134 = I1 + I3

So,

I2 = I1 + I3

Since R1 and R34 are in parallel, So

V134 = V1 = V34

R3 and R4 are in series, So V34 = V3 + V4

(V3 and V4 will not be always equal since it will depend on the value of R3 and R4)

V1 = V3 + V4

E = V2 + V134

E = V1 + V2 = V2 + V34 = V2 + V3 + V4

Correct option is B, C and G