Consider three resistors with unequal resistances connected in parallel to a battery. which of the following statements are
true?

1)the voltage across each of the resistors is the same and is equal in magnitude to the voltage of the battery.
2)the current flowing through each of the resistors is the same and is equal to the current supplied by the battery.
3)the equivalent resistance of the combination of resistors is greater than the resistance of any one of the three resistors.
4)the algebraic sum of the voltages across the three resistors is equal to the voltage supplied by the battery.
5)the equivalent resistance of the combination of resistors is less than the resistance of any one of the three resistors.
6)the algebraic sum of the currents flowing through each of the three resistors is equal to the current supplied by the battery.

1, 5 and 6 are true

Explanation:

Let's analyze each statement:

1)The voltage across each of the resistors is the same and is equal in magnitude to the voltage of the battery.  --> TRUE. When three resistors are connected in parallel to a battery, each one is connected to the two terminals of the battery, so the voltage across each resistor is the same as the voltage of the battery.

2)The current flowing through each of the resistors is the same and is equal to the current supplied by the battery.  --> FALSE. In a parallel circuit, the current flowing through each resistor is different, as given by Ohm's law:

The resistors have same voltage across them (V) but different resistance (R), so the current through them is not the same.

3)The equivalent resistance of the combination of resistors is greater than the resistance of any one of the three resistors.  --> FALSE. It's actually the opposite: the equivalent resistance for a parallel combination of resistors is

and this implies that is smaller than any of R1, R2 and R3.

4)The algebraic sum of the voltages across the three resistors is equal to the voltage supplied by the battery.  --> FALSE. As stated in 1), the voltage across each resistor is actually equal to the voltage of the battery, so this statement cannot be true.

5)The equivalent resistance of the combination of resistors is less than the resistance of any one of the three resistors.  --> TRUE. As stated in #3, the equivalent resistance is smaller than the resistance of any one of the three resistor.

6)The algebraic sum of the currents flowing through each of the three resistors is equal to the current supplied by the battery. --> TRUE. In fact, the total current flowing out from the battery split into the three separate branches containing the three resistors: since the current must be conserved, it means that the sum of the currents flowing through each of the three resistors is equal to the current supplied by the battery.

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