Question

Many resistors are connected purely in parallel to a 17 battery and the power output of the battery is 169 Watts. One resistor is removed (but the rest remain connected in parallel to the same battery) and the current coming out of the battery is 3.3 amps with that resistor removed. What was the value of the resistance of the removed resistor in Ohms?

Answer 1

Hi,

Hope you are doing well.

The above arrangement can be represented as following circuit.

Where,

R is the resistor Removed and R_p is the effective resistance of all remaining resistors connected in parallel.

CASE 1;

When Resistor R is removed, the total resistance remaining in the circuit will be R_p.

Given that,

Current from battery,

Voltage of battery,

According to Ohm's Law, resistance R_p ,

CASE 2;

When Resistor R is on the circuit, the total effective resistance of the circuit will be R_effective is given by,

( and are parallel.)

Given that,

Substituting value for , we get,

Also, Given that,

Power output from battery when all resistors are in parallel,

We know that, Power is given by,

Where,

is the Voltage of battery (V).

is the current from battery (A).

Given that,

Voltage of battery,

Current from battery when all resistors are connected in parallel,

According to Ohm's Law,

From equation (1), substituting value for R_effective , We get,

Resistance of resistor Removed ,

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