Question #43771

A potentiometer circuit is used to measure the stopping potential of a photoelectric cell. The driver cell has an electromotive force $E_d = 30 \text{ V}$ and an internal resistance $r = 10 \ \Omega$. The potentiometer wire $AB$ has a length $L = 100 \text{ cm}$ and a resistance $R_0 = 10 \ \Omega$ at the ambient temperature $T_0$. The wire has a temperature coefficient of resistance $\alpha = 0.01 \text{ K}^{-1}$. When current flows, the wire heats up, and its steady-state temperature rise $\Delta T$ above the ambient temperature is proportional to the electrical power $P$ dissipated in it, given by $\Delta T = \beta P$, where $\beta = 5 \text{ K W}^{-1}$. The photoelectric cell is illuminated by monochromatic light of wavelength $\lambda = 124 \text{ nm}$. The work function of the emitter material is $\Phi = 4.0 \text{ eV}$. Assuming $hc = 1240 \text{ eV nm}$, find the balance length $l$ on the potentiometer wire for the stopping potential of the photoelectric cell in the steady state.