Three identical light-bulb filaments, each of resistance Rb when glowing, are connected in series to a dc power supply whose internal resistance is negligible. A student wishes to measure simultaneously (i) the current through the middle bulb and (ii) the potential difference across that same bulb, using a real ammeter of internal resistance ra and a real voltmeter of internal resistance Rv.
Address the following questions.
(a) Describe explicitly how the ammeter and the voltmeter should be connected so that each reads the intended quantity while allowing both instruments to remain in the circuit at the same time.
(b) Qualitatively analyze how the simultaneous presence of both meters alters the current through, and the brightness of, all three bulbs compared with the original circuit in which no meters were present. In your explanation, refer to the relative magnitudes of ra, Rv, and Rb.
(c) Suppose ra is not negligible compared with Rb. Propose two practical modifications—one involving the meters themselves and one involving the measurement procedure—that would reduce the overall measurement error. Justify how each modification mitigates the disturbance introduced by the meters.