Question

With the help of a circuit diagram, deduce the equivalent resistance of two resistances connected in series .
Two resistances are connected in series as shown in the diagram:
What is the current through the 5 ohm resistance ?
What is the current through R?
What is the value of R?
What is the value of V?​

Answer 1

Answer:

Fig. shows two resistances R1 and R2 Connected in series with a battery of V

Let the p.d. across R1 is V1 and p.d. across R2 is v2.

s.t. V = V1 + V2 ------------(1)

Let the equivalent resistance be R and current flowing through whole circuit is I.

By ohm’s law,

V/I = R

V = I × R --------(2)

Applying ohm’s law to both R1 and R2,

V1 = I × R1 -------------(3)

V2 = I × R2 -------------(4)

From eqs. (1), (2), (3) and (4), we get

I × R = I × R1 + I × R2

I × R = I × (R1 + R2)

R = R1 + R2

(b)

(i) Current through 5 Ω resistor = 10/5 = 2 A

(ii) Since 5 Ω resistor and R are connected in series, so same current flows through so, current through R = 2 A

(iii) V = IR

R = V/I = 6/2 = 3 Ω

(iv) V = 10 + 6 = 16 V

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