Learn equivalent resistance with examples, and short circuit definition. Practice equation to calculate combination of resistors in series and parallel circuits.

- Two resistors connected without other joint present between them are said to be in series.
- Resistors R
_{1}and R_{2}are in series combination as no other joint is present in figure.

- In this figure since a joint is present so, this is not a series combination.

- Current \(I\) will be same in R
_{1}and R_{2}because current will not divide due to absence of any other joint.

- Current \(I\) will divide due to presence of joint.

- Since a joint is present between A and A' and similarly between B and B' due to this same current will not flow in R
_{1}and R_{2}. - Such combination is known as parallel combination.

- Consider a circuit as shown in figure.

- This circuit is neither simple series nor simple parallel combination because it contains elements of both.

A R1 and R2 in series

B R2 and R3 in series

C R1 and R3 in series

D None

- In series connection current through each resistor is same.

- Some amount of charge Q exists on resistor R
_{1}. The same charge Q must also enter in R_{2}otherwise the charge will accumulate between resistors.

- The potential difference applied across the series combination of resistors divide between the resistors.

\(\Delta V=IR_1+IR_2\)

or, \(\Delta V=IR_{eq}\)

where \(R_{eq}=R_1+R_2\)

- The equivalent resistance for more than two resistors connected in series is

\(R_{eq}=R_1+R_2+R_3+...\)

A \(15\,\Omega\)

B \(16\,\Omega\)

C \(17\,\Omega\)

D \(18\,\Omega\)

- When two points of a circuit are connected together by a conducting wire, they are said to be short circuited.
- The connecting wire is assumed to have zero resistance.

- Voltage difference between terminal B and D is zero.

\(V_{BD}=0\)

- Hence, there will be no current in resistances R
_{2}and R_{3}.

**Note- **The shorted components are not damaged, they will function normally when short circuit is removed.

A \(6\,\Omega\)

B \(4\,\Omega\)

C \(2.2\,\Omega\)

D \(3\,\Omega\)

- Potential difference across each resistor is same.

- Total current \((I)= I_1+I_2\)

\(I=\dfrac{\Delta V}{R_{eq}},\,I_1=\dfrac{\Delta V}{R_1},\,I_2=\dfrac{\Delta V}{R_2}\)

\(\dfrac{\Delta V}{R_{eq}}=\dfrac{\Delta V}{R_1}+\dfrac{\Delta V}{R_2}\)

\(\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\)

- For more than two resistance connected in parallel

\(\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+...\)

A \(9\,\Omega\)

B \(8\,\Omega\)

C \(\dfrac{15}{11}\,\Omega\)

D \(\dfrac{11}{15}\,\Omega\)

- Consider combination of four resistors connected as shown in figure.

Step - 1

For loop (I) R and R in parallel

\(\dfrac{1}{R'}=\dfrac{1}{R}+\dfrac{1}{R}\)

\(R'=\dfrac{R}{2}\)

Step - 2

For loop (II) R and R in parallel

\(\dfrac{1}{R''}=\dfrac{1}{R}+\dfrac{1}{R}\)

\(R''=\dfrac{R}{2}\)

Step - 3

R' and R'' in series

\(R_{eq}=R'+R''\)

\(R_{eq}=\dfrac{R}{2}+\dfrac{R}{2}\)

\(R_{eq}=R\)

A \(5\,\Omega\)

B \(15\,\Omega\)

C \(20\,\Omega\)

D \(10\,\Omega\)