Question 14 Marks

Two or more resistances are connected in series or in parallel or both, depending upon whether we want to increase or decrease the circuit resistance.

The two or more resistances are said to be connected in series if the current flowing through each resistor is the same.
i. When the three resistors each of resistance R ohm are connected in series then what will be the equivalent resistance?
ii. There is a wire of length 20 cm and having resistance $20 \Omega$ cut into 4 equal pieces and then joined in series. What is equivalent resistance?
iii. In the following circuit, find the equivalent resistance between A and $\mathrm{B}(\mathrm{R}=2 \Omega)$

OR
In the given circuit, what is the current in each resistor?

Answer

i. In series combination, R_s = R₁ + R₂ + R₃ = R + R + R = 3R.
ii. The equivalent resistance is where the total resistance is connected either in parallel or in series.Resistance of each wire $=\frac{20}{4}=5 \Omega$
Equivalent resistance in series
$\mathrm{R}_{\mathrm{s}}=5+5+5+5=20 \Omega$
iii. All are in series, $\mathrm{R}_{\mathrm{S}}=5 \mathrm{R}=5 \times 2=10 \Omega$
OR
$\mathrm{R}_{\mathrm{s}}=1+2+3=6 \Omega$
$I=\frac{18}{6}=3 \mathrm{~A}$

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