Physics
Physics
Problem
A circuit consists of a 4 Ω resistor, a 6 Ω resistor and a small lamp connected in series with an ideal cell. The lamp is marked 3 V, 0.30 A. (i) Determine the resistance of the lamp when it glows at its marked rating. (ii) Calculate the emf the cell must supply so that the lamp operates at its rated conditions when connected with the two resistors in series. (iii) If the 4 Ω resistor is removed from the circuit while the cell emf remains the same, calculate the new current through the lamp and state whether the lamp will be brighter, dimmer or fail to glow. Justify your answer with calculations. a. (i) Determine the resistance of the lamp from its marked rating 3 V, 0.30 A. b. (ii) Calculate the emf required from the cell so that the lamp receives its rated voltage when connected in series with 4 Ω and 6 Ω resistors. c. (iii) The 4 Ω resistor is removed while the cell emf remains the same. Calculate the new current through the lamp and state, with reason, whether the lamp becomes brighter, dimmer or fails to glow.Intuitive explanation
The key to this problem is understanding how components in series share voltage according to their resistance, and recognizing that a lamp's brightness depends on the power it receives. Start by using the lamp's rated values to find its resistance as a fixed property, then apply Ohm's law and Kirchhoff's voltage law to find what emf is needed to push the correct current through the entire series chain. Finally, when you remove a resistor, the total resistance drops, current increases, and you'll need to compare the new power delivered to the lamp against its rated power to judge brightness.
Intuitive explanation
The key to this problem is understanding how components in series share voltage according to their resistance, and recognizing that a lamp's brightness depends on the power it receives. Start by using the lamp's rated values to find its resistance as a fixed property, then apply Ohm's law and Kirchhoff's voltage law to find what emf is needed to push the correct current through the entire series chain. Finally, when you remove a resistor, the total resistance drops, current increases, and you'll need to compare the new power delivered to the lamp against its rated power to judge brightness.