Write the differences between series and parallel connections of resistors.

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Series ConnectionParallel Connection
$(1)$ Resistors are connected end-to-end such that the same electric current flows through each resistor.$(1)$ Resistors are connected between the same two points such that the potential difference across each resistor is the same.
$(2)$ The potential difference across each resistor is different.$(2)$ The electric current flowing through each resistor is different.
$(3)$ The equivalent resistance is given by $R_{eq} = R_{1} + R_{2} + \dots + R_{n}$.$(3)$ The equivalent resistance is given by $\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \dots + \frac{1}{R_{n}}$.
$(4)$ The equivalent resistance is greater than the largest individual resistance in the circuit.$(4)$ The equivalent resistance is smaller than the smallest individual resistance in the circuit.
$(5)$ If one resistor fails, the entire circuit breaks.$(5)$ If one resistor fails, the other branches continue to function.

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